Anti-triangular and anti-m-Hessenberg forms for Hermitian matrices and pencils

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Author(s) : Christian Mehl

The paper is published : Linear Algebra Appl., 317: 143-176, 2000

MSC 2000

15A21 Canonical forms, reductions, classification
15A57 Other types of matrices

Abstract :
Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions which anti-triangular and anti-m-Hessenberg forms for general (including singular) Hermitian pencils can be obtained under unitary equivalence transformations.

Keywords : Hermitian pencils, Hermitian matrix, Schur-form