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<! Made by Html Translation Ver 1.0><html><head><title> 基本矩阵运算元 </title></head><body BACKGROUND="../img1/bg0000.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/bg0000.gif"><script language="JAVASCRIPT"><!--if (navigator.onLine){document.write("<!-- Spidersoft WebZIP Ad Banner Insert -->");document.write("<TABLE width=100% border=0 cellpadding=0 cellspacing=0>");document.write("<TR>");document.write("<TD>");document.write("<ILAYER id=ad1 visibility=hidden height=60></ILAYER>");document.write("<NOLAYER>");document.write("<IFRAME SRC='http://www.spidersoft.com/ads/bwz468_60.htm' width=100% height=60 marginwidth=0 marginheight=0 hspace=0 vspace=0 frameborder=0 scrolling=no></IFRAME>");document.write("</NOLAYER>");document.write("</TD>");document.write("</TR>");document.write("</TABLE>");document.write("<!-- End of Spidersoft WebZIP Ad Banner Insert-->");} //--></script><!-- Spidersoft WebZIP Ad Banner Insert --><!-- End of Spidersoft WebZIP Ad Banner Insert--><font COLOR="#0000FF"><h1>5.1.1 基本矩阵运算元</h1></font><hr><p>我们在第二章已说明过 MATLAB 的运算是以阵列(array)及矩阵 <font FACE="Times New Roman">(matrix) </font>方式在做运算，而这二者在MATLAB的 基本运算性质不同，阵列强调元素对元素的运算，而矩阵则采用线性代数的运算方式。我们就来说明矩阵运算 的特点。 <br></p><p>以下将阵列及矩阵的运算符号及其意义列出 </p><table BORDER="1"> <tr> <td WIDTH="106">阵列运算符号</td> <td WIDTH="104">矩阵运算符号 </td> <td WIDTH="72">功能</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">+</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">+</font> </td> <td WIDTH="72">加</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">-</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">-</font> </td> <td WIDTH="72">减</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">.*</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">*</font> </td> <td WIDTH="72">乘</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">./</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">/</font> </td> <td WIDTH="72">左除</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">.\</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000">\</font> </td> <td WIDTH="72">右除</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">.^</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">^</font> </td> <td WIDTH="72">次方</td> </tr> <tr> <td WIDTH="106"><p align="center"><font COLOR="#FF0000" FACE="Times New Roman">.</font><font COLOR="#FF0000">'</font> </td> <td WIDTH="104"><p align="center"><font COLOR="#FF0000">'</font> </td> <td WIDTH="72">转置</td> </tr></table><p>利用这些运算符号即可进行以下的矩阵运算。 </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A=[2 5 1; 7 3 8; 4 5 21; 16 13 0];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A' % A</font><font COLOR="#FF0000">的转置矩阵</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">A =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">2 7 4 16</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">5 3 5 13</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">1 8 21 0<br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A=[4 -1 3]; B=[-2 5 2];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> dot_prod = sum(A.*B) % </font><font COLOR="#FF0000">二个阵列做内积</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">dot_prod =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-7</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> c=dot(A,B) % </font><font COLOR="#FF0000">以</font><font COLOR="#FF0000" FACE="Times New Roman">dot</font><font COLOR="#FF0000">函数也可做内积运算</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">c =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-7<br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A=[4; -1; 3];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> dot_prod = sum(A'.*B); % </font><font COLOR="#FF0000">如果</font><font COLOR="#FF0000" FACE="Times New Roman">A</font><font COLOR="#FF0000">是行阵列则先做转置，再做内积 <br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> F=[2 5 -1]; G=[0 1 -3];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> out_prod=F'*G; % </font><font COLOR="#FF0000">二矩阵做外积<br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A=[2,5,1; 0,3,-1];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> B=[1,0,2; -1,4,-2; 5,2,1];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> C=A*B % </font><font COLOR="#FF0000">矩阵相乘，注意二个矩阵的大小须相容</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">C =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">2 22 -5</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-8 10 -7<br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A=[2 1; 4 3];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> A^2 % </font><font COLOR="#FF0000">矩阵次方</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">4 1</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">16 9<br></font></p><hr><a HREF="ch5_1.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch5_1.htm"><p><img SRC="../img1/lastpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/lastpage.gif" BORDER="0" WIDTH="42" HEIGHT="42"></a> <a HREF="ch5_1_2.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch5_1_2.htm"><img SRC="../img1/nextpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/nextpage.gif" BORDER="0" HSPACE="10" WIDTH="42" HEIGHT="42"></a> <a HREF="../index.html" tppabs="http://webclass.ncu.edu.tw/~junwu/index.html"><img SRC="../img1/outline.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/outline.gif" BORDER="0" HSPACE="6" WIDTH="42" HEIGHT="42"></a><br><font SIZE="2" COLOR="#AA55FF">上一页 下一页 讲义大纲 </font><layer src="http://www.spidersoft.com/ads/bwz468_60.htm" visibility="hidden" id="a1" width="600" onload="moveToAbsolute(ad1.pageX,ad1.pageY); 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