# qz

Version:

Performs the QZ decomposition of a pair of square matrices.

## 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)

## A

Square matrix.

## B

Square matrix of the same size as A.

## type

Type of decomposition to perform.

Name Description
'real' Performs the real QZ decomposition. A and B must be real square matrices. MathScript stores the real and imaginary parts of the complex eigenvectors in two consecutive columns.
'complex' Performs the complex QZ decomposition.

## S

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

Upper triangular matrix of the same size as A.

## Q

Unitary matrix of the same size as A.

## Z

Unitary matrix of the same size as A.

## R

Right generalized eigenvectors.

## L

Left generalized eigenvectors.

## QZ Decomposition of a Matrix Pair

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).

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices