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qz

Version:
    Last Modified: March 15, 2017

    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)

    Inputs

    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.

    Outputs

    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


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