Version:

Last Modified: March 15, 2017

Performs the QZ decomposition of a pair of square matrices.

[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)

Square matrix.

Square matrix of the same size as A.

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. |

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.

Upper triangular matrix of the same size as A.

Unitary matrix of the same size as A.

Unitary matrix of the same size as A.

Right generalized eigenvectors.

Left generalized eigenvectors.

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