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

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

Research output: Contribution to journalArticlepeer-review

12 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 languageEnglish
Pages (from-to)242-269
Number of pages28
JournalLinear Algebra and Its Applications
Volume416
Issue number2-3
DOIs
StatePublished - 15 Jul 2006

Keywords

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

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