Lemma diagonal_nonzero_iff_transpose_nonzero { n : nat } (A : Matrix R n n) : diagonal_all_nonzero A <-> diagonal_all_nonzero (transpose A). Proof. split ; intros H; unfold diagonal_all_nonzero, transpose, flip; apply H. 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.