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考研數(shù)學(xué)之線性代數(shù)知識點以及重要性質(zhì)指導(dǎo)
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 smallbs
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發(fā)表于 2010-08-25 20:45
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[html]<
 style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">數(shù)學(xué)中，線性代數(shù)這門課程的概念多、定理多、符號多、運算規(guī)律多、內(nèi)容相互縱橫交錯，知識前后緊密聯(lián)系。下面就對線代每章中一些具體知識點以及重要性質(zhì)作一闡述：</P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>一、行列式</B></P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">行列式的核心內(nèi)容是求行列式，包括具體行列式的計算和抽象行列式的計算，其中具體行列式的計算又有低階和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 15px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 16px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823125.gif"></SUB>階兩種類型。主要方法是應(yīng)用行列式按行或者列展開定理和化為上下三角行列式求解，還可能用到的方法包括：行列式的定義（<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 13px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 15px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823126.gif"></SUB>階行列式的值為取自不同行、不同列的<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 15px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 16px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image001.gif" name="AsyncWordImage"></SPAN></SUB>個元素的乘積的代數(shù)和）、性質(zhì)<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 40px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823128.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823129.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 39px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823130.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 21px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823131.gif"></SUB>（其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823132.gif"></SUB>為矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 19px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823133.gif"></SUB>的特征值）、行列式的性質(zhì)（如“數(shù)乘行列式等于用此數(shù)乘一行列式中的某一行或某一列”）。對于抽象行列式的求值，考點不在求行列式，而在于考慮<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823134.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 28px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823135.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 37px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823136.gif"></SUB>等的相關(guān)性質(zhì)。</P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">二、矩陣</STRONG></P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">矩陣中除可逆陣、伴隨陣、分塊陣、初等陣等重要概念外，主要也是運算，其運算分兩個層次，一是運用矩陣的性質(zhì)對抽象矩陣進(jìn)行運算，二是具體矩陣的數(shù)值運算。</P><P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">下面的表格分類列出了逆矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 29px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823137.gif"></SUB>、伴隨矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823138.gif"></SUB>、矩陣轉(zhuǎn)置<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 23px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image009.gif" name="AsyncWordImage"></SPAN></SUB>的性質(zhì)以供區(qū)別記憶：</P> <table style="BORDER-COLLAPSE: collapse; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px" border=1 cellSpacing=0 cellPadding=0 width=550> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>行列式性質(zhì)</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>特征值性質(zhì)（<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 15px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823139.gif"></SUB>為矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823140.gif"></SUB>的特征值）</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>運算性質(zhì)</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>秩的性質(zhì)</P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">轉(zhuǎn)置矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823143.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 50px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823144.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 27px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823145.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 87px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823146.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 109px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823147.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 118px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823148.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 138px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823149.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 110px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823150.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 134px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823151.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823152.gif"></SUB></P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">逆矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823153.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 82px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 47px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823154.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 41px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823155.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">伴隨矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823156.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 89px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823157.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 42px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823158.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823159.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823160.gif"></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 30px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image026.gif" name="AsyncWordImage"></SPAN></SUB>三者之間有一個既好記又好用的性質(zhì)</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823161.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823162.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 113px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823163.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 163px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 75px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823164.gif"></SUB></P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">數(shù)乘矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823165.gif"></SUB>、矩陣之積<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823166.gif"></SUB>及矩陣之和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 47px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823167.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 88px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823168.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 108px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823169.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 31px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823170.gif"></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823171.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 78px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823172.gif"></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 47px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823174.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823176.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823177.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823178.gif"></SUB>則有：<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 106px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823179.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 21px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823180.gif"></SUB>是可逆矩陣則有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 91px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823181.gif"></SUB>；同樣，若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 16px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823182.gif"></SUB>可逆則有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 100px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823183.gif"></SUB></P></td> </tr> </table> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">三、向量、線性方程組</STRONG></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">向量與線性方程組的內(nèi)容聯(lián)系很密切，很多知識點相互之間都有或明或暗的相關(guān)性。復(fù)習(xí)這兩章最有效的方法就是徹底弄清楚諸多知識點之間的內(nèi)在聯(lián)系，因為這樣做首先能夠保證做到真正意義上的理解，同時也是熟練掌握和靈活運用的前提。以下給出這部分主要知識點：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">三個雙重定義：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.秩的定義</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a.矩陣秩的定義：矩陣中非零子式的最高階數(shù)。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b.向量組秩定義：向量組的極大線性無關(guān)組中的向量個數(shù)。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.線性相關(guān)無關(guān)的定義</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a. 對于一組向量<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 95px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823184.gif"></SUB>，若存在不全為零的數(shù)<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 82px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823185.gif">使得<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 201px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823186.gif">成立，則相量組線性相關(guān)，否則向量組線性無關(guān)，即上述等式當(dāng)且僅當(dāng)<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823187.gif">全為0時才成立。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b. 向量組<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 94px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 30px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823188.gif">線性相關(guān)ó向量組中至少存在一個向量可由其余<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 15px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 16px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image001.gif" name="AsyncWordImage"></SPAN>-1個向量線性表出；線性無關(guān)ó向量組中沒有一個向量可由其余的向量線性表出。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">3．線性方程組的兩種形式</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a. 矩陣形式：<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823189.gif"></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b. 向量形式：<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 232px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823190.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>兩條性質(zhì)：</B></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.對于方陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 42px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823191.gif"></SUB>有：方陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823192.gif"></SUB>可逆ó存在方陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823194.gif"></SUB>使得<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 110px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823195.gif"></SUB>ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 59px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823196.gif"></SUB>ó<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN></SUB>的行列向量組均線性無關(guān)ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 74px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823197.gif"></SUB>ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 69px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823198.gif"></SUB>可由克萊姆法則判斷有唯一解，而<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 54px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823199.gif"></SUB>僅有零解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">對于一般矩陣<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 42px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 27px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image062.gif" name="AsyncWordImage"></SPAN>則有：<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 72px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823200.gif">ó<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量組線性無關(guān)ó<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 54px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image069.gif" name="AsyncWordImage"></SPAN>僅有零解，<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 56px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823201.gif">有唯一解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.齊次線性方程組<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 54px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image069.gif" name="AsyncWordImage"></SPAN>是否有非零解對應(yīng)于系數(shù)矩陣<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量組是否線性相關(guān)，而非齊次線性方程組<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 56px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image071.gif" name="AsyncWordImage"></SPAN>是否有解對應(yīng)于<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 19px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823202.gif">是否可以由<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量組線性表出。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">以上兩條性質(zhì)可視為是將線性相關(guān)、行列式、秩、線性方程組幾部分知識聯(lián)系在一起的橋梁。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>關(guān)于秩的一些結(jié)論</B>：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 145px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823203.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823204.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 177px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823205.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 178px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823206.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 174px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823207.gif"></SUB>；若有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 35px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823208.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 32px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823209.gif"></SUB>滿足<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 51px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823210.gif"></SUB>，則<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 103px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823211.gif"></SUB>；若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823212.gif"></SUB>是可逆矩陣，則有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 99px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823213.gif"></SUB>；同樣若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823214.gif"></SUB>可逆則有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 98px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823215.gif"></SUB>。非齊次線性方程組<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 61px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823216.gif"></SUB>有唯一解則對應(yīng)齊次方程組<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823217.gif"></SUB>僅有零解，若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 53px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823218.gif"></SUB>有無窮多解則<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 58px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image087.gif" name="AsyncWordImage"></SPAN></SUB>有非零解；若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 69px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image068.gif" name="AsyncWordImage"></SPAN></SUB>有兩個不同的解則<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 58px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image087.gif" name="AsyncWordImage"></SPAN></SUB>有非零解；若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 17px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 19px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image015.gif" name="AsyncWordImage"></SPAN></SUB>是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 46px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823219.gif"></SUB>矩陣而<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 80px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823220.gif"></SUB>則<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 59px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823221.gif"></SUB>一定有解，而且當(dāng)<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 49px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823222.gif"></SUB>時是唯一解，當(dāng)<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 52px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823223.gif"></SUB>時是無窮多解，而若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 70px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823224.gif"></SUB>則<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 51px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823225.gif"></SUB>沒有解或有唯一解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">四、特征值與特征向量</STRONG></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">本章知識要點如下：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.特征值和特征向量的定義及計算方法就是記牢一系列公式，如:<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 62px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823226.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 49px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823227.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 86px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823228.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 103px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823229.gif"></SUB>和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 98px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823230.gif"></SUB>。在歷年真題中常用到下列性質(zhì)：若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823231.gif"></SUB>階矩陣<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823232.gif"></SUB>有<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 18px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image101.gif" name="AsyncWordImage"></SPAN></SUB>個特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823233.gif"></SUB><SPAN class=Apple-converted-space> </SPAN><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 44px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823235.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823237.gif"></SUB>，則有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823238.gif"></SUB>；若矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 17px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 19px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image015.gif" name="AsyncWordImage"></SPAN></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823239.gif"></SUB>，則<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823240.gif"></SUB>、<B><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823241.gif"></SUB></B>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 68px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823242.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 43px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823243.gif"></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 30px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image026.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823244.gif"></SUB>分別有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823245.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 29px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823246.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 54px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823247.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 41px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823248.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 47px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823249.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 32px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 45px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823250.gif"></SUB>，且對應(yīng)特征向量等于<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823252.gif"></SUB>所對應(yīng)的特征向量，而若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 32px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823253.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 32px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823254.gif"></SUB>分別為矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>的特征值，則<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 52px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823256.gif"></SUB>不一定為<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 38px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823257.gif"></SUB>的特征值。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.相似矩陣及其性質(zhì)。定義式為<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 88px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823258.gif"></SUB>，需要區(qū)分矩陣的相似、等價與合同：矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>與矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>等價的定義式是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 79px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823259.gif"></SUB>，其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823260.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823261.gif"></SUB>為可逆矩陣，此時矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>可通過初等變換化為矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 20px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image084.gif" name="AsyncWordImage"></SPAN></SUB>，并有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 81px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823262.gif"></SUB>；當(dāng)<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 74px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823263.gif"></SUB>中的<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image126.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823264.gif"></SUB>互逆時就變成了矩陣相似的定義式，即有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 90px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823265.gif"></SUB>，此時滿足<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 93px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823266.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 68px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823267.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 164px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823268.gif"></SUB>，并且<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 20px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image084.gif" name="AsyncWordImage"></SPAN></SUB>有相同的特征值。矩陣合同的定義是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 85px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823269.gif"></SUB>，其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 15px; BORDER-LEFT-WIDTH: 0px" alt="考研數(shù)學(xué)線代部分復(fù)習(xí)指導(dǎo) " src="http://img1.gtimg.com/edu/pics/29823/29823270.gif"></SUB>為可逆矩陣。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">由以上定義可看出等價、合同、相似三者之間的關(guān)系：若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>與<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>合同或相似則<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>與<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>必等價，反之不成立；合同與等價之間沒有必然聯(lián)系。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">3.矩陣可相似對角化的條件。包括兩個充要條件和兩個充分條件，充要條件（1）是<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 13px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 15px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image002.gif" name="AsyncWordImage"></SPAN></SUB>階矩陣<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>有<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER- |
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