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

Abstract

We classify all linear operators $A:V\to V$ satisfying $(Au,v)=(u,A^{r}v)$ and all linear operators satisfying $(Au,A^{r}v)=(u,v)$ 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.

References in corpus (5)

• Classification problems for system of forms and linear mappings
• Canonical matrices of bilinear and sesquilinear forms
• Canonical matrices of isometric operators on indefinite inner product spaces
• Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form
• Classification of linear mappings between indefinite inner product spaces