Matrix polynomial
= Matrix polynomial
{title2=$p(A)=\sum_{j=0}^m c_jA^j$}
Evaluate a scalar <polynomial> on a square <matrix> by replacing its variable with that <matrix> and its constant term with a multiple of the <identity matrix>. Powers of the same <matrix> <commute>, so $p(A)q(A)=(pq)(A)$. For an <eigenvector> $Av=\lambda v$, $p(A)v=p(\lambda)v$.