svd

Singular value decomposition.

Syntax

S          = svd(X)
[U, S, V]  = svd(X)
[U, S, V]  = svd(X, 0)        % economy size
[U, S, V]  = svd(X, 'econ')   % economy size

Description

Computes the SVD of X: orthogonal/unitary U, diagonal nonnegative S, orthogonal/unitary V such that X = U*S*V'. With one return, gives just the singular values as a vector.

The economy form (passing 0 or 'econ' as the second argument) returns U and V truncated to the smaller dimension — significantly cheaper for tall or wide matrices.

Examples

[U, S, V] = svd([1 2; 3 4; 5 6]);
size(U)                  % [3 3]    full form
[U, S, V] = svd([1 2; 3 4; 5 6], 'econ');
size(U)                  % [3 2]    economy

See also

• eig — Eigenvalues and eigenvectors.
• qr — QR decomposition.
• rank — Numerical rank of a matrix.
• norm — Vector or matrix norm.
• cond — Condition number of a matrix.