User`s guide

Singular Value Decomposition

5-405

5Singular Value Decomposition

Purpose Factor a matrix using singular value decomposition.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The Singular Value Decomposition block factors the M-by-N input matrix A

such that

where U is an M-by-P matrix, V is an N-by-P matrix, S is a length-P vector, and

P is defined as min(M,N).

When M = N, U and V are both M-by-M unitary matrices. When M > N, V is an

N-by-N unitary matrix, and U is an M-by-N matrix whose columns are the first

N columns of a unitary matrix. When N > M, U is an M-by-M unitary matrix,

and V is an M-by-N matrix whose columns are the first N columns of a unitary

matrix. In all cases, S is a 1-D vector of positive singular values having length

P. The output is always sample-based.

Length-N row inputs are treated as length-N columns.

[U,S,V] = svd(A,0) % Equivalent MATLAB code for M > N

Note that the first (maximum) element of output S is equal to the 2-norm of the

matrix A.

You can enable the

U and V output ports by selecting the Output the singular

vectors

parameter.

Dialog Box

Compute singular vectors

Enables the

U and V output ports when selected.

∗

diag S()V

⋅=