MATLAB Language Matrix decompositions Singular value decomposition


Given an m times n matrix A with n larger than m. The singular value decomposition

[U,S,V] = svd(A);

computes the matrices U,S,V.

The matrix U consists of the left singular eigenvectors which are the eigenvectors of A*A.' while V consists of the right singular eigenvalues which are the eigenvectors of A.'*A. The matrix S has the square roots of the eigenvalues of A*A.' and A.'*A on its diagonal.

If m is larger than n one can use

[U,S,V] = svd(A,'econ');

to perform economy sized singular value decomposition.