Endomorphism/Determinant/Definition

Determinant of a linear map

Let $K$ denote a field, and let $V$ denote a $K$-vector space of finite dimension. Let

$\phi :V⟶V$

be a linear mapping, which is described by the matrix $M$, with respect to a basis. Then

$det\phi :=detM$

is called the determinant of the linear mapping $\phi$.