Singular value decomposition of a general real matrix.  The matrix is decomposed as U∙S∙VT.

Syntax

U,S,V = SVD(M)

Argument

Name

Description

M

A general m by n matrix of real values.

Outputs

Name

Description

U

An m by m orthogonal matrix.

S

An m by n diagonal matrix.

V

An n by n orthogonal matrix.

Example

Find the singular value decomposition of a matrix.

Syntax

M = [1,2;3,4;5,6]; // Given matrix

u,s,v = SVD(M);

Result

u =  0.22985        -0.88346         0.40825

      0.52474        -0.24078         -0.8165

      0.81964          0.4019         0.40825

s =  9.5255     0

      0          0.5143

      0          0

v =  0.61963    0.78489

      0.78489   -0.61963

Comments

Every matrix has a singular value decomposition.

See Also:

Csky

LU