Operators on positive semidefinite inner product spaces

Victor A. Bovdi; Tetiana Klymchuk; Tetiana Rybalkina; Mohamed A. Salim; Vladimir V. Sergeichuk

doi:10.1016/j.laa.2020.03.004

paper

Operators on positive semidefinite inner product spaces

arXiv:2003.06919 · doi:10.1016/j.laa.2020.03.004

Abstract

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$ . For an arbitrary system of semiunitary spaces and linear mappings on/between them, we give an algorithm that reduces their matrices to canonical form.

28 pages