QZ Decomposition (Not in Base Package)

Performs the QZ decomposition of a pair of square matrixes. You can use this polymorphic VI to perform the QZ decomposition of real matrixes or complex matrixes. The data types you wire to the A and B inputs determine the polymorphic instance to use. Details  

Real QZ Decomposition

	A is a square real matrix.
	B is the second square real matrix.
	Eigenvectors returns a complex matrix that contains the generalized eigenvectors in its columns.
	Q is an orthogonal matrix. Where trans(Q) is the transpose matrix of Q, Q satisfies the following conditions: trans(Q)AZ is a Hessenberg matrix. trans(Q)BZ is an upper triangular matrix.
	Z is an orthogonal matrix. Where trans(Q) is the transpose matrix of Q, Z satisfies the following conditions: trans(Q)AZ is a Hessenberg matrix. trans(Q)BZ is an upper triangular matrix.
	Alpha returns the numerators of the generalized eigenvalues of matrix pair (A,B). If Betai is nonzero, Alphai/Betai is a generalized eigenvalue of (A,B).
	Beta returns the denominators of the generalized eigenvalues of matrix pair (A,B). If Betai is nonzero, Alphai/Betai is a generalized eigenvalue of (A,B).
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Complex QZ Decomposition

	A is a square complex matrix.
	B is the second square complex matrix.
	Eigenvectors returns a complex matrix that contains the generalized eigenvectors in its columns.
	Q is a unitary matrix. Where trans(Q) is the conjugate transpose matrix of Q, Q satisfies the condition that trans(Q)AZ and trans(Q)BZ are upper triangular matrixes.
	Z is a unitary matrix. Where trans(Q) is the conjugate transpose matrix of Q, Z satisfies the condition that trans(Q)AZ and trans(Q)BZ are upper triangular matrixes.
	Alpha returns the numerators of the generalized eigenvalues of matrix pair (A,B). If Betai is nonzero, Alphai/Betai is a generalized eigenvalue of (A,B).
	Beta returns the denominators of the generalized eigenvalues of matrix pair (A,B). If Betai is nonzero, Alphai/Betai is a generalized eigenvalue of (A,B).
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

QZ Decomposition Details

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

A = QHZ^H

B = QTZ^H

where A and B are n-by-n square matrixes, Z^H is the conjugate transpose of matrix Z, T is an n-by-n upper triangular matrix, and H is a Hessenberg matrix. Refer to the Hessenberg Decomposition VI for information about Hessenberg matrixes.