= MATLAB svd =

The '''`svd`''' function calculates the [[LinearAlgebra/SingularValueDecomposition|SVD decomposition]] of any matrix.

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== 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 [[MATLAB/Pinv|pinv]] does.

To calculate the rank ''k'' [[LinearAlgebra/LowRankApproximation|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'`.



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