Definition scalar_mult_row { m n : nat} (r : ⟦ m ⟧%stn) (s : F) (mat : Matrix F m n) : Matrix F m n. Proof. intros i j. induction (stn_eq_or_neq i r). - exact (s * (mat i j))%ring. - exact (mat i j). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices.