General linear group

Matrix determinant is a homomorphism

The Matrix determinant when applied to the General linear group

is a group epimorphism, #m/thm/group where the codomain is the multiplicative group of the underlying field

Proof

From properties of the Matrix determinant, for any :

Hence is a homomorphism. For any , there exists with . Hence is an epimorphism.

Properties

#state/tidy | #lang/en | #SemBr