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

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.

published proceedings

  • Linear Algebra and its Applications

author list (cited authors)

  • Sykes, D., & Zelenko, I.

citation count

  • 2

complete list of authors

  • Sykes, David||Zelenko, Igor

publication date

  • April 2020