MATLAB Function Reference    
qz

QZ factorization for generalized eigenvalues

Syntax

Description

The qz function gives access to intermediate results in the computation of generalized eigenvalues.

[AA,BB,Q,Z,V] = qz(A,B) for square matrices A and B, produces upper triangular matrices AA and BB, unitary matrices Q and Z containing the products of the left and right transformations, such that Q*A*Z = AA, and Q*B*Z = BB, and the generalized eigenvector matrix V.

[AA,BB,Q,Z,V] = qz(A,B,flag) for real matrices A and B, produces one of two decompositions depending on the value of flag:

'complex'
 Produces a possibly complex decomposition with a triangular AA. 'complex' is the default.
'real'
 Produces a real decomposition with a quasitriangular AA, containing 1-by-1 and 2-by-2 blocks on its diagonal.

If AA is triangular, the alphas and betas comprising the generalized eigenvalues are the diagonal elements of AA and BB so that

If AA is quaditriangular, it is necessary to solve 2-by-2 generalized problems to obtain the actual eigenvalues.

For complex matrices A and B, AA and BB are always triangular.

Algorithm

For real QZ on real A and real B, eig uses the LAPACK DGGES routine. If you request the fifth output V, eig also uses DTGEVC.

For complex QZ on real or complex A and B, eig uses the LAPACK ZGGES routine. If you request the fifth output V, eig also uses ZTGEVC.

See Also

eig

References

[1]  Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide, Third Edition, SIAM, Philadelphia, 1999.


 quiver3 rand