Let \(T\colon V\to V\) be a linear map and \(V\) a finite-dimensional vector space. Then the determinant of a linear map is given by
\begin{equation*} \det T = \det A, \end{equation*}where \(A\) is a basis-representation matrix of \(T\).
Remark
- This definition is reasonable since the value does not change under basis transformation.