svd - singular value decomposition

Calling Sequence

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])

Parameters

• X : a real or complex matrix
• s : real vector (singular values)
• S : real diagonal matrix (singular values)
• U,V : orthogonal or unitary square matrices (singular vectors).
• tol : real number

Description

produces a diagonal matrix S , of the same dimension as X and with nonnegative diagonal elements in decreasing order, and unitary matrices U and V so that X = U*S*V'.

or

produces the "economy size" decomposition. If X is m-by-n with m > n, then only the first n columns of U are computed and S is n-by-n.

by itself, returns a vector s containing the singular values.

gives in addition rk, the numerical rank of X i.e. the number of singular values larger than tol.

The default value of tol is the same as in rank.

Examples

X=rand(4,2)*rand(2,4)
svd(X)
sqrt(spec(X*X'))
 

See Also

rank  qr  colcomp  rowcomp  sva  spec  

Used Function

svd decompositions are based on the Lapack routines DGESVD for real matrices and ZGESVD for the complex case.