# qz (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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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.

Details

Examples

## 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.

 'real' Performs the real QZ decomposition. A and B must be real square matrices. LabVIEW stores the real and imaginary parts of the complex eigenvectors in two consecutive columns. 'complex' (default) Performs the complex QZ decomposition.

## 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).

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

## Examples

A = reshapemx(1:16, 4, 4);
B = magic(4);
[S, T, Q, Z] = qz(A, B)

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