Canonical forms for doubly structured matrices and pencils

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Author(s) : Christian Mehl , Volker Mehrmann , Hongguo Xu

The paper is published : Electron. J. Linear Algebra, 7: 112-151, 2000

MSC 2000

15A21 Canonical forms, reductions, classification
15A22 Matrix pencils

Abstract :
In this paper, canonical forms under structure-preserving equivalence transformations are presented for matrices and matrix pencils that have a multiple structure, which is either an H-self-adjoint or H-skew-adjoint structure, where the matrix H is a complex nonsingular Hermitian or skew-Hermitian matrix. Matrices and pencils of such multiple structures arise, for example, in quantum chemistry in Hartree-Fock models or random phase approximation.

Keywords : Indefinite innder product, selfadjoint matrix, skew-adjoint matrix, matrix pencil, canonical form