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<h4 class="subsection">20.1.2 Creating Permutation Matrices</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>q</var> is a permutation vector of length <var>n</var>, the expression
<pre class="example">       P = eye (n) (:, q);
</pre>
   <p>will create a permutation matrix - a special matrix object.
<pre class="example">     eye (n) (q, :)
</pre>
   <p>will also work (and create a row permutation matrix), as well as
<pre class="example">     eye (n) (q1, q2).
</pre>
   <p>For example:
<pre class="example">       eye (4) ([1,3,2,4],:)
     &rArr;
     Permutation Matrix
     
        1   0   0   0
        0   0   1   0
        0   1   0   0
        0   0   0   1
     
       eye (4) (:,[1,3,2,4])
     &rArr;
     Permutation Matrix
     
        1   0   0   0
        0   0   1   0
        0   1   0   0
        0   0   0   1
</pre>
   <p>Mathematically, an identity matrix is both diagonal and permutation matrix. 
In Octave, <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.

<pre class="example">       eye (3)
     &rArr;
     Diagonal Matrix
     
        1   0   0
        0   1   0
        0   0   1
     
       eye(3)(1:3,:)
     &rArr;
     Permutation Matrix
     
        1   0   0
        0   1   0
        0   0   1
</pre>
   <p>Some other built-in functions can also return permutation matrices.  Examples include
<dfn>inv</dfn> or <dfn>lu</dfn>.

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