% Algorithm 1: Outer Product Gaussian Elimination (Alg. 3.2.1)
function [U, L] = outer_product_gaussian_elimination(A)

[n, m] = size(A);
if n ~= m
    error('Matrix is not squared!')
end
    
 if det(A) == 0
    error('Matrix is not nonsingular!') 
 end
 
 for k = 1 : n-1
     rows = k + 1 : n;
     A(rows, k) = A(rows, k)/A(k, k);
     A(rows, rows) = A(rows, rows) - A(rows, k) * A(k, rows);
 end
 
U = triu(A);
L = tril(A, -1) + eye(n);