% m16_factorizations.m - tour of matrix factorizations

    A = magic(5)		% magic square matrix
    sum(A,1)
    sum(A,2)
  
    [Q,R] = qr(A)		% QR factorization
    Q*R - A
  
    [L,U,P] = lu(A)		% LU factorization with pivoting
    P*A - L*U
  
    R = chol(A)			% Cholesky factorization
    R = chol(A'*A)
    R'*R - A'*A
  
    eig(A)			% eigenvalue decomposition
    [V,D] = eig(A)
    A*V - V*D
  
    eig(A+A')			% orthogonal eigenvalue decomposition
    [Q,D] = eig(A+A')
    A+A' - Q*D*Q'
  
    eig(A)			% Schur triangularization
    [Q,T] = schur(A)
    A - Q*T*Q'

    svd(A)			% singular value decomposition (SVD)
    [U,S,V] = svd(A)
    A - U*S*V'