Definition upper_triangular_right_inverse_construction { n : nat } (mat : Matrix F n n) := transpose (λ i : (stn n), (back_sub _ mat (@identity_matrix F n i))).
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Nat. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices. Require Import UniMath.Algebra.GaussianElimination.Elimination.