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<h4 class="subsection" id="Creating-Permutation-Matrices-1"><span>21.1.2 Creating Permutation Matrices<a class="copiable-link" href="#Creating-Permutation-Matrices-1"> ¶</a></span></h4>
<p>For creating permutation matrices, Octave does not introduce a new function,
but rather overrides an existing syntax: permutation matrices can be
conveniently created by indexing an identity matrix by permutation vectors.
That is, if <var class="var">q</var> is a permutation vector of length <var class="var">n</var>, the expression
</p>
<div class="example">
<pre class="example-preformatted"> P = eye (n) (:, q);
</pre></div>
<p>will create a permutation matrix - a special matrix object.
</p>
<div class="example">
<pre class="example-preformatted">eye (n) (q, :)
</pre></div>
<p>will also work (and create a row permutation matrix), as well as
</p>
<div class="example">
<pre class="example-preformatted">eye (n) (q1, q2).
</pre></div>
<p>For example:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"> eye (4) ([1,3,2,4],:)
⇒
Permutation Matrix
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
eye (4) (:,[1,3,2,4])
⇒
Permutation Matrix
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
</pre></div></div>
<p>Mathematically, an identity matrix is both diagonal and permutation matrix.
In Octave, <code class="code">eye (n)</code> returns a diagonal matrix, because a matrix
can only have one class. You can convert this diagonal matrix to a permutation
matrix by indexing it by an identity permutation, as shown below.
This is a special property of the identity matrix; indexing other diagonal
matrices generally produces a full matrix.
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"> eye (3)
⇒
Diagonal Matrix
1 0 0
0 1 0
0 0 1
eye(3)(1:3,:)
⇒
Permutation Matrix
1 0 0
0 1 0
0 0 1
</pre></div></div>
<p>Some other built-in functions can also return permutation matrices. Examples
include
<em class="dfn">inv</em> or <em class="dfn">lu</em>.
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