<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>transpose(Matrix) -- transpose a matrix</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="___Tree__Node.html">next</a> | <a href="_transpose_lp__List_rp.html">previous</a> | <a href="___Tree__Node.html">forward</a> | <a href="_transpose_lp__List_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>transpose(Matrix) -- transpose a matrix</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>transpose f</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_transpose.html" title="transpose a table or a matrix">transpose</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>Here is an example.<table class="examples"><tr><td><pre>i1 : S = ZZ/10007[x,y,z];</pre>
</td></tr>
<tr><td><pre>i2 : f = matrix{{x^3,x*y^2},{y*x^2,y^3}}
o2 = | x3 xy2 |
| x2y y3 |
2 2
o2 : Matrix S <--- S</pre>
</td></tr>
<tr><td><pre>i3 : g = transpose f
o3 = {-3} | x3 x2y |
{-3} | xy2 y3 |
2 2
o3 : Matrix S <--- S</pre>
</td></tr>
</table>
The output of <tt>transpose</tt> is a map between the duals of the original source and target free modules. See:<table class="examples"><tr><td><pre>i4 : degrees f
o4 = {{{0}, {0}}, {{3}, {3}}}
o4 : List</pre>
</td></tr>
<tr><td><pre>i5 : degrees g
o5 = {{{-3}, {-3}}, {{0}, {0}}}
o5 : List</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div><tt>transpose</tt> works only for maps between free modules. Use <tt>dual</tt> for more general maps.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dual.html" title="dual module or map">dual</a> -- dual module or map</span></li>
</ul>
</div>
</div>
</body>
</html>
