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Main Title: On doubly structured matrices and pencils that arise in linear response theory
Author(s): Mehl, Christian
Mehrmann, Volker
Xu, Hongguo
Type: Research Paper
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.
Subject(s): selfadjoint matrix
skew-adjoint matrix
matrix pencil
Hartree-Fock model
anti-triangular form
canonical form
condensed form
Hamiltonian pencil
Issue Date: 5-Nov-2001
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
15A21 Canonical forms, reductions, classification
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2001, 713
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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