Author(s) :
Christian Mehl
,
Volker Mehrmann
,
Hongguo Xu
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 713-2001
MSC 2000
- 65F15 Eigenvalues, eigenvectors
-
15A21 Canonical forms, reductions, classification
Abstract :
We discuss matrix pencils with a double symmetry structure
that arise in the Hartree-Fock model in quantum chemistry. We derive
anti-triangular condensed forms from which the eigenvalues
can be read off.
Ideally these would be condensed forms under
unitary equivalence transformations
that can be turned into stable (structure preserving) numerical methods.
For the pencils under consideration this is a difficult task and not always
possible. We present necessary and sufficient
conditions when this is possible. If this is not possible
then we show how we can include other transformations that allow to reduce
the pencil to an almost anti-triangular form.
Keywords :
Selfadjoint matrix, skew-adjoint matrix, matrix pencil, Hartree-Fock model, anti-triangular form , canonical form, condensed form,skew-Hamiltonian/Hamiltonian pencil