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arXiv · 2012.04052

Classification of linear operators satisfying $(Au,v)=(u,A^rv)$ or $(Au,A^rv)=(u,v)$ on a vector space with indefinite scalar product

Victor Senoguchi Borges·Iryna Kashuba·Vladimir V. Sergeichuk·Eduardo Ventilari Sodré·André Zaidan
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Abstract

We classify all linear operators $A:V\to V$ satisfying $(Au,v)=(u,A^rv)$ and all linear operators satisfying $(Au,A^rv)=(u,v)$ with $r=2,3,\dots$ on a complex, real, or quaternion vector space with scalar product given by a nonsingular symmetric, skew-symmetric, Hermitian, or skew-Hermitian form.

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Victor Senoguchi Borges, Iryna Kashuba, Vladimir V. Sergeichuk, Eduardo Ventilari Sodré, André Zaidan. 2020-12-07. Classification of linear operators satisfying $(Au,v)=(u,A^rv)$ or $(Au,A^rv)=(u,v)$ on a vector space with indefinite scalar product. https://doi.org/10.1016/j.laa.2020.12.005

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