Performs the QZ decomposition of a pair of square matrices. The data types you wire to the A and B inputs determine the polymorphic instance to use.


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The following expressions define the QZ decomposition of a matrix pair (A, B).

A = QHZH B = QTZH

where A and B are n-by-n square matrices, ZH is the conjugate transpose of matrix Z, T is an n-by-n upper triangular matrix, and H is an n-by-n upper Hessenberg matrix if the decomposition type is Generalized Hessenberg or a quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal blocks if the decomposition type is Generalized Schur. Refer to the Hessenberg Decomposition VI for information about Hessenberg matrices.

If B is singular, matrix pair (A, B) has an infinite generalized eigenvalue, in other words, Betai is zero. If αA–βB is singular for all α and β, matrix pair (A, B) is singular and has an indeterminate generalized eigenvalue, in other words, both Betai and Alphai are zeros. This VI cannot order the generalized eigenvalues if there are indeterminate generalized eigenvalues.