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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Operatoren für konjugierte Transposition und Transposition</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Genius-Handbuch"><link rel="up" href="ch08.html" title="Chapter 8. Matrizen in GEL"><link rel="prev" href="ch08.html" title="Chapter 8. Matrizen in GEL"><link rel="next" href="ch08s03.html" title="Lineare Algebra"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Operatoren für konjugierte Transposition und Transposition</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch08.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Matrizen in GEL</th><td width="20%" align="right"> <a accesskey="n" href="ch08s03.html">Next</a></td></tr></table><hr></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-matrix-transpose"></a>Operatoren für konjugierte Transposition und Transposition</h2></div></div></div><p lang="en">
You can conjugate transpose a matrix by using the <code class="literal">'</code> operator. That is
the entry in the
<code class="varname">i</code>th column and the <code class="varname">j</code>th row will be
the complex conjugate of the entry in the
<code class="varname">j</code>th column and the <code class="varname">i</code>th row of the original matrix.
For example:
</p><pre lang="en" class="programlisting">[1,2,3]*[4,5,6]'
</pre><p lang="en">
We transpose the second vector to make matrix multiplication possible.
If you just want to transpose a matrix without conjugating it, you would
use the <code class="literal">.'</code> operator. For example:
</p><pre lang="en" class="programlisting">[1,2,3]*[4,5,6i].'
</pre><p lang="en">
</p><p lang="en">
Note that normal transpose, that is the <code class="literal">.'</code> operator, is much faster
and will not create a new copy of the matrix in memory. The conjugate transpose does
create a new copy unfortunately.
It is recommended to always use the <code class="literal">.'</code> operator when working with real
matrices and vectors.
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