Definition scalar_mult_row_matrix {n : nat} (r : ⟦ n ⟧%stn) (s : F) : Matrix F n n. Proof. intros i. induction (stn_eq_or_neq i r). - exact (const_vec s *pw @stdb_vector F _ i). - exact (@stdb_vector F _ i). 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.