A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator Academic Article

abstract

• Motivated by a problem in local differential geometry of Cauchy--Riemann (CR) structures of hypersurface type, we find a canonical form for pairs consisting of a nondegenerate Hermitian form and a self-adjoint antilinear operator, or, equivalently, consisting of a nondegenerate Hermitian form and a symmetric bilinear form. This generalizes the only previously known results on simultaneous normalization of such pairs, namely, the results of Benedetti and Cragnolini (1984) on simultaneous diagonalization of these pairs in the case where the Hermitian form is positive definite and of Hong and Horn (1986), where a criterion for simultaneous diagonalization is given.

authors

• Zelenko, Igor

published proceedings

• LINEAR ALGEBRA AND ITS APPLICATIONS

altmetric score

• 0.25

author list (cited authors)

• Sykes, D., & Zelenko, I.

citation count

• 2

complete list of authors

• Sykes, David||Zelenko, Igor

publication date

• January 2020

publisher

• Elsevier  Publisher

published in

• Linear Algebra and Its Applications  Journal

keywords

• Antilinear Operators
• Canonical Forms
• Indefinite Hermitian Forms
• Pencils
• Uniformly Levi Degenerate Cr Structures

Digital Object Identifier (DOI)

• 10.1016/j.laa.2019.12.018

start page

• 32

end page

• 61

volume

• 590

URL

• http://dx.doi.org/10.1016/j.laa.2019.12.018