Definition:Characteristic Polynomial of Linear Operator/Definition 1

Definition
Let $A$ be a commutative ring with unity.

Let $M$ be a free module over $A$ of finite rank $n > 0$.

Let $\phi : M \to M$ be a linear operator.

The characteristic polynomial of $\phi$ is the characteristic polynomial of the relative matrix of $\phi$ with respect to a basis of $M$.

Also see

 * Equivalence of Definitions of Characteristic Polynomial of Linear Operator