Basic classes of matrices with respect to quaternionic indefinite inner product spaces

D. Alpay; A. C.M. Ran; L. Rodman

doi:10.1016/j.laa.2005.11.010

Basic classes of matrices with respect to quaternionic indefinite inner product spaces

D. Alpay
, A. C.M. Ran
, L. Rodman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Basic classes of matrices or linear transformations in finite dimensional quaternionic vector spaces with a regular indefinite inner product are introduced and studied. The classes include plus matrices, selfadjoint, skew-adjoint, and unitary matrices. In particular, results are proved concerning extensions of invariant semidefinite subspaces. Canonical form for unitary matrices is developed and subsequently applied to stability of periodic Hamiltonian systems.

Original language	English
Pages (from-to)	242-269
Number of pages	28
Journal	Linear Algebra and Its Applications
Volume	416
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2005.11.010
State	Published - 15 Jul 2006

Keywords

Canonical forms
Indefinite inner product
Invariant semidefinite subspaces
Plus matrix
Quaternionic vector space
Selfadjoint
Skew-adjoint
Unitary

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2005.11.010

Cite this

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abstract = "Basic classes of matrices or linear transformations in finite dimensional quaternionic vector spaces with a regular indefinite inner product are introduced and studied. The classes include plus matrices, selfadjoint, skew-adjoint, and unitary matrices. In particular, results are proved concerning extensions of invariant semidefinite subspaces. Canonical form for unitary matrices is developed and subsequently applied to stability of periodic Hamiltonian systems.",

keywords = "Canonical forms, Indefinite inner product, Invariant semidefinite subspaces, Plus matrix, Quaternionic vector space, Selfadjoint, Skew-adjoint, Unitary",

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AU - Alpay, D.

AU - Ran, A. C.M.

AU - Rodman, L.

PY - 2006/7/15

Y1 - 2006/7/15

N2 - Basic classes of matrices or linear transformations in finite dimensional quaternionic vector spaces with a regular indefinite inner product are introduced and studied. The classes include plus matrices, selfadjoint, skew-adjoint, and unitary matrices. In particular, results are proved concerning extensions of invariant semidefinite subspaces. Canonical form for unitary matrices is developed and subsequently applied to stability of periodic Hamiltonian systems.

AB - Basic classes of matrices or linear transformations in finite dimensional quaternionic vector spaces with a regular indefinite inner product are introduced and studied. The classes include plus matrices, selfadjoint, skew-adjoint, and unitary matrices. In particular, results are proved concerning extensions of invariant semidefinite subspaces. Canonical form for unitary matrices is developed and subsequently applied to stability of periodic Hamiltonian systems.

KW - Canonical forms

KW - Indefinite inner product

KW - Invariant semidefinite subspaces

KW - Plus matrix

KW - Quaternionic vector space

KW - Selfadjoint

KW - Skew-adjoint

KW - Unitary

UR - https://www.scopus.com/pages/publications/33747043583

U2 - 10.1016/j.laa.2005.11.010

DO - 10.1016/j.laa.2005.11.010

M3 - Article

AN - SCOPUS:33747043583

SN - 0024-3795

VL - 416

SP - 242

EP - 269

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -

Basic classes of matrices with respect to quaternionic indefinite inner product spaces

Abstract

Keywords

ASJC Scopus subject areas

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