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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="MatMinPoly"></a>
MatMinPoly
</h2>

Returns the minimal polynomial of a matrix.

<p><p>

<h3>
Syntax:
</h3>
<pre>f := MatMinPoly(M);</pre>

<p>

<table>
<tr>
<td>matrix</td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
<tr>
<td>Polynomial</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#EltMinPoly">EltMinPoly</a>, <a href="kashref.html#MatCharPoly">MatCharPoly</a>

<p>

<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the minimal polynomial of
\left(\begin{array}{cccc} 0 & 1 & 0 & -1 1 & 0 & 1 & 0
0 & 1 & 0 & 1 -1 & 0 & 1 & 0 \end{array}right)
\in {Z}^{4 \times 4}. 
<pre>

kash> M := Mat(Z,[[0,1,0,-1],[1,0,1,0],[0,1,0,1],[-1,0,1,0]]);
[ 0  1  0 -1]
[ 1  0  1  0]
[ 0  1  0  1]
[-1  0  1  0]
kash> MatMinPoly(M);
x^2 - 2
kash> M^2;
> [2 0 0 0]
[0 2 0 0]
[0 0 2 0]
[0 0 0 2]

</pre>

<p>


<hr>

<p>
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