Polynomial of an endomorphism

Definition

Let $F$ be a field, let $V$ be a vector space over $F$, and let $T \colon V \to V$ be an endomorphism. Let $p(x) = c_0 + c_1 x + \cdots + c_d x^d$ be a polynomial in $F[x]$. The value of $p$ at $T$ is the endomorphism $$p(T) = c_0 \id_V + c_1 T + c_2 T^2 + \cdots + c_d T^d,$$ where $T^k$ is the composition of $k$ copies of $T$. For an $n \times n$ matrix $A$, $p(A) = c_0 I_n + c_1 A + \cdots + c_d A^d$ in the same way.