Lemma matrix_mult_vectors {n : nat} (vec1 vec2 : Vector R n) : ((row_vec vec1) ** (col_vec vec2)) = weq_matrix_1_1 (Σ (vec1 ^ vec2)). Proof. apply funextfun; intro i; apply funextfun; intro j; reflexivity. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Combinatorics.FiniteSequences. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.RigsAndRings.