Matrix polynomial ($p(A)={\sum }_{j=0}^m{c}_j{A}^j$)

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 $Av=\lambda v$, $p(A)v=p(\lambda )v$.