QZ factorization for generalized eigenvalues
Syntax
[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.
[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
The qz function 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)
Arguments
A,B
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Square matrices.
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AA,BB
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Upper triangular matrices.
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Q,Z
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Transformation matrices.
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V
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Matrix whose columns are eigenvectors.
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Algorithm
Complex generalizations of the EISPACK routines QZHES, QZIT, QZVAL, and QZVEC implement the QZ algorithm.
See Also
eig Eigenvalues and eigenvectors
References
[1] Moler, C. B. and G.W. Stewart, "An Algorithm for Generalized Matrix Eigenvalue Problems", SIAM J. Numer. Anal., Vol. 10, No. 2, April 1973.
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