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Preprint 713-2001

On doubly structured matrices and pencils that arise in linear response theory

Source file is available as :   Postscript Document

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

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