MATLAB svd
The svd function calculates the SVD decomposition of any matrix.
Contents
Usage
To solve the problem Ax = b for any size matrix A, try:
[U, S, V] = svd(A); S_inv = diag(1./diag(S)); x = V * S_inv * U' * b;
This is effectively what pinv does.
To calculate the rank k approximation of a matrix A, try:
[U, S, V] = svd(A); U_k = U(:, 1:k) S_k = S(1:k, 1:k) V_k = V(:, 1:k) A_k = U_k * S_k * V_k'
The original A can be returned by U*S*V'.