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

$\varphi \colon V\longrightarrow V$

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

${}\det \varphi :=\det M\,$

is called the determinant of the linear mapping ${}\varphi$.