# gsvd

Version:

Performs generalized singular value decomposition (SVD) of a matrix pair.

## Syntax

x = gsvd(A, B)
[U, V, R, C, S] = gsvd(A, B)
[U, V, R, C, S] = gsvd(A, B, 0)

Matrix.

## B

Matrix. A and B must have the same number of columns.

## 0

Directs MathScript to perform generalized SVD in the economy size format. You can also use 'econ' instead of 0.

## x

Generalized singular values. x is a vector.

## U

An orthogonal matrix of the generalized SVD.

## V

An orthogonal matrix of the generalized SVD.

## R

A square matrix of the generalized SVD.

## C

A diagonal matrix of the generalized SVD.

## S

A diagonal matrix of the generalized SVD.

## Equations

The following equations define the generalized singular value decomposition of a matrix pair (A, B):

A = UCR'

B = VSR'

where U and V are orthogonal matrices, and R is a square matrix. Let k be the rank of the matrix [A; B]. Then the first k diagonal elements of matrix C'C + S'S are ones and all other elements are zeros. The square roots of the first k diagonal elements of C'C and S'S determine the numerators and denominators, respectively, of the generalized singular values.

If A is an m-by-p matrix, and B is an n-by-p matrix, then [U, V, R, C, S] = gsvd(A, B) returns U as an m-by-m matrix, V as an n-by-n matrix, R as a p-by-p matrix, C as an m-by-p matrix, and S as an n-by-p matrix. If you specify 0, MathScript performs generalized SVD in the economy size format. In other words, [U, V, R, C, S] = gsvd(A, B, 0) returns U as an m-by-min(m, p) matrix, V as an n-by-min(n, p) matrix, R as a p-by-p matrix, C as a min(m, p)-by-p matrix, and S as a min(n, p)-by-p matrix.

A = reshapemx(1:12, 4, 3);
B = magic(3);
X = gsvd(A, B)

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices