title: Computing the inverse of a polynomial matrix
body: <p>I am working with a system of the following structure:</p>
  
  <p><code><strong>L</strong> (k,m) = <strong>A<sub>2</sub></strong> k<sup>2</sup> + <strong>A<sub>1</sub></strong> k + <strong>A<sub>0</sub></strong> - m <strong>B</strong></code></p>
  
  <p>I have the matrices (<code><strong>A<sub>2</sub></strong></code>, <code><strong>A<sub>1</sub></strong></code>, <code><strong>A<sub>0</sub></strong></code>, and <code><strong>B</strong></code>) numerically and would like to compute coefficient matrices for <code><strong>L<sup>-1</sup></strong></code> such that I can evaluate <code><strong>L<sup>-1</sup></strong></code> for a given combination (<code>k,m</code>) without computing a matrix inverse each time. Could someone point me on the right direction for this type of algorithm / manipulation? I'm not even sure I know the correct search terms to search the linear algebra literature on the subject. I'm using MATLAB.</p>