qz

Purpose

QZ factorization for generalized eigenvalues.

Synopsis

[AA,BB,Q,Z,V] = qz(A,B)

Description

The qz function gives access to what are normally only intermediate results in the computation of generalized eigenvalues. For square matrices A and B, the statement

[AA,BB,Q,Z,V] = qz(A,B)
produces upper triangular matrices AA and BB, and matrices Q and Z containing the products of the left and right transformations, such that

Q*A*Z = AA
Q*B*Z = BB
qz also returns the generalized eigenvector matrix V.

The generalized eigenvalues are the diagonal elements of AA and BB so that

A*V*diag(BB) = B*V*diag(AA)

Algorithm

Complex generalizations of the EISPACK routines QZHES, QZIT, QZVAL, and QZVEC implement the QZ algorithm.

See Also

eig

References

[1] C. B. Moler and G.W. Stewart, "An Algorithm for Generalized Matrix Eigenvalue Problems", SIAM J. Numer. Anal., Vol. 10, No. 2, April 1973.

(c) Copyright 1994 by The MathWorks, Inc.