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arXiv · 2003.06919

Operators on positive semidefinite inner product spaces

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

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Victor A. Bovdi, Tetiana Klymchuk, Tetiana Rybalkina, Mohamed A. Salim, Vladimir V. Sergeichuk. 2020-03-15. Operators on positive semidefinite inner product spaces. https://doi.org/10.1016/j.laa.2020.03.004

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