MATLAB Function Reference |
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] = qz(A,B)
for square matrices A
and B
, produces upper quasitriangular matrices AA
and BB
, and unitary matrices Q
and Z
such that Q*A*Z = AA
, and Q*B*Z = BB
. For complex matrices, AA
and BB
are triangular.
[AA,BB,Q,Z,V,W] = qz(A,B)
also produces matrices V
and W
whose columns are generalized eigenvectors.
qz(A,B,flag)
for real matrices A
and B
, produces one of two decompositions depending on the value of flag
:
If AA
is triangular, the diagonal elements of AA
and BB
,
are the generalized eigenvalues that satisfy
are the element-wise ratios of alpha
and beta
.
If AA
is not triangular, it is necessary to further reduce the 2-by-2 blocks to obtain the eigenvalues of the full system.
Algorithm
For full matrices A
and B
, qz
uses the LAPACK routines listed in the following table.
See Also
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 (http://www.netlib.org/lapack/lug/ lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.
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