Definition:Determinant/Linear Operator

Definition
Let $V$ be a finite-dimensional vector space over a field $K$.

Let $A: V \to V$ be a linear transformation of $V$.

The determinant $\det \left({A}\right)$ of $A$ is defined to be the determinant of any matrix of $A$ relative to some basis.

Also see

 * Determinant of Linear Transformation is Well Defined