Lemma sum_id_pointwise_prod { n : nat } (v : Vector R n) (i : ⟦ n ⟧%stn) : Σ ((identity_matrix i) *pw v) = (v i). Proof. apply sum_stdb_vector_pointwise_prod. 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.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors.