Section MapMatrixSpaces.
Variables (aF rF : fieldType) (f : {rmorphism aF -> rF}).
Local Notation "A ^f" := (map_mx f A) : ring_scope.

Lemma Gaussian_elimination_map m n (A : 'M_(m, n)) :
Gaussian_elimination A^f = ((col_ebase A)^f, (row_ebase A)^f, \rank A).