qz (MathScript RT Module Function)
Owning Class: linalgebra
Requires: MathScript RT Module
Syntax
[S, T, Q, Z] = qz(A, B)
[S, T, Q, Z] = qz(A, B, type)
[S, T, Q, Z, R, L] = qz(A, B)
[S, T, Q, Z, R, L] = qz(A, B, type)
Description
Performs the QZ decomposition of a pair of square matrices.
Inputs
| Name | Description | ||||
|---|---|---|---|---|---|
| A | Specifies a square matrix. | ||||
| B | Specifies a square matrix of the same size as A. | ||||
| type | Specifies the type of decomposition to perform.
|
Outputs
| Name | Description |
|---|---|
| S | Returns an upper triangular matrix of the same size as A. If type is 'real', S returns a quasi-upper triangular matrix of the same size as A. |
| T | Returns an upper triangular matrix of the same size as A. |
| Q | Returns a unitary matrix of the same size as A. |
| Z | Returns a unitary matrix of the same size as A. |
| R | Returns the right generalized eigenvectors. |
| L | Returns the left generalized eigenvectors. |
Details
qz performs the QZ decomposition of a matrix pair (A, B) such that Q*A*Z = S and Q*B*Z = T, where Q and Z are unitary matrices, and S and T are upper triangular matrices. The matrix pair (S, T) has the same generalized eigenvalues as the matrix pair (A, B). If S is an upper triangular matrix, the diagonal elements of S and T are the numerators and denominators, respectively, of the generalized eigenvalues of the matrix pair (A, B).
Examples
A = reshapemx(1:16, 4, 4);
B = magic(4);
[S, T, Q, Z] = qz(A, B)