File: transpose.htm

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<HTML>
<HEAD>
<TITLE>TRANSPOSE</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">

<P><A NAME="transpose"></A>
<font size="+3" color="green"><B>TRANSPOSE</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
vout = &lt;&minus;v</CODE>
</TD></TR>
</table></p>
<p>
 The transpose operator, <code>&lt;&minus;</code>, is a unary operator
 that produces the transpose of a matrix, that is, the rows and columns are
 interchanged.</p>
<p>
 Suppose the matrix <code>M</code> has M rows and N columns. Then 
 <code>&lt;-M</code> has N rows and M columns, where <code>(&lt;-M)[i,j] = M[j,i]</code> for
 <code>i = 1,2,...,N</code> and <code>j = 1,2,...,M</code>.</p>
<P>
 <font size="+1" color="green">Example</font></p>
<P>
 Let
 <pre>
     |  1  2  3 |
 M = |  4  5  6 |
     |  7  8  9 |
     | 10 11 12 |
 </pre>
 then
 <pre>
       |  1  4  7 10 |
 &lt;-M = |  2  5  8 11 |
       |  3  6  9 12 |
 </pre></p>
</BODY>
</HTML>