Version:

Last Modified: March 15, 2017

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

x = gsvd(A, B)

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

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

Matrix.

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

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

Generalized singular values. x is a vector.

An orthogonal matrix of the generalized SVD.

An orthogonal matrix of the generalized SVD.

A square matrix of the generalized SVD.

A diagonal matrix of the generalized SVD.

A diagonal matrix of the generalized SVD.

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