singular value decomposition
s=svd(X) [U,S,V]=svd(X) [U,S,V]=svd(X,0) (obsolete) [U,S,V]=svd(X,"e") [U,S,V,rk]=svd(X [,tol])
a real or complex matrix
real vector (singular values)
real diagonal matrix (singular values)
orthogonal or unitary square matrices (singular vectors).
[U,S,V] = svd(X) produces a diagonal matrix
S , of the same dimension as
X and with
nonnegative diagonal elements in decreasing order, and unitary
V so that
X = U*S*V'.
[U,S,V] = svd(X,0) produces the "economy
size" decomposition. If
X is m-by-n with m >
n, then only the first n columns of
U are computed
S is n-by-n.
s= svd(X) by itself, returns a vector
containing the singular values.
[U,S,V,rk]=svd(X,tol) gives in addition
rk, the numerical rank of
X i.e. the number of
singular values larger than
The default value of
tol is the same as in
svd decompositions are based on the Lapack routines DGESVD for real matrices and ZGESVD for the complex case.