The singular value decomposition (SVD) of an m-by-n matrix A is given by
where U and V are orthogonal (unitary) and is an m-by-n diagonal matrix with real diagonal elements, , such that
The are the singular values of A and the first min(m,n) columns of U and V are the left and right singular vectors of A.
The singular values and singular vectors satisfy
where and are the ith columns of U and V, respectively.
A single driver routine, PxGESVD , computes the ``economy size'' or ``thin'' singular value decomposition of a general nonsymmetric matrix (see table 3.4). Thus, if A is m-by-n with m>n, then only the first n columns of U are computed and is an n-by-n matrix. For a detailed discussion of the ``thin'' singular value decomposition, refer to [71, p. 72,].
Currently, only PSGESVD and PDGESVD are provided.
Table 3.4: Driver routines for standard eigenvalue and singular value problems