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<TITLE> 基本矩阵运算元 </TITLE>
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<H1>5.1.1 基本矩阵运算元</H1>
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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。
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以下将阵列及矩阵的运算符号及其意义列出
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<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><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">+</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">+</FONT></CENTER>
</TD><TD WIDTH=72>加</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">-</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">-</FONT></CENTER>
</TD><TD WIDTH=72>减</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">.*</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">*</FONT></CENTER>
</TD><TD WIDTH=72>乘</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">./</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">/</FONT></CENTER>
</TD><TD WIDTH=72>左除</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">.\</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000>\</FONT></CENTER>
</TD><TD WIDTH=72>右除</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">.^</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">^</FONT></CENTER>
</TD><TD WIDTH=72>次方</TD></TR>
<TR><TD WIDTH=106><CENTER><FONT COLOR=#FF0000 FACE="Times New Roman">.</FONT><FONT COLOR=#FF0000>'</FONT></CENTER>
</TD><TD WIDTH=104><CENTER><FONT COLOR=#FF0000>'</FONT></CENTER>
</TD><TD WIDTH=72>转置</TD></TR>
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利用这些运算符号即可进行以下的矩阵运算。
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A=[2 5 1;
7 3 8; 4 5 21; 16 13 0];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A'
% A</FONT><FONT COLOR=#FF0000>的转置矩阵</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">A =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 2 7 4 16</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 5 3 5 13</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 1 8 21 0<BR>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A=[4 -1 3];
B=[-2 5 2];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> dot_prod =
sum(A.*B) % </FONT><FONT COLOR=#FF0000>二个阵列做内积</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">dot_prod =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> -7</FONT>
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<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>
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<FONT COLOR=#FF0000 FACE="Times New Roman">c =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> -7<BR>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A=[4; -1;
3];</FONT>
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<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
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> F=[2 5 -1];
G=[0 1 -3];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> out_prod=F'*G;
% </FONT><FONT COLOR=#FF0000>二矩阵做外积<BR>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A=[2,5,1;
0,3,-1];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> B=[1,0,2;
-1,4,-2; 5,2,1];</FONT>
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<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>
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<FONT COLOR=#FF0000 FACE="Times New Roman">C =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 2 22 -5</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> -8 10 -7<BR>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A=[2 1; 4
3];</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> A^2
% </FONT><FONT COLOR=#FF0000>矩阵次方</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans =</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 4 1</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman"> 16 9<BR>
</FONT><HR>
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