Real Matrix Polynomials
Definition
A (real) matrix
polynomial of degree
$d$ is a function $p: \R ^{n \times n} \to
\R ^{n \times n}$ for which there exists a
finite sequence $(c_0, c_1, \dots , c_{d-1}, c_d)
\in \R ^{d+1}$ satisfying,
\[
p(A) = c_0 I + c_1 A^1 + c_2 A^2 + \cdots + c_dA^d,
\]