Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form

Abstract

Let $V$ be a vector space over a field $\mathbb{F}$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb{F}=\mathbb{C}$, then we give canonical matrices of isometric and selfadjoint operators on $V$ using known classifications of isometric and selfadjoint operators on a complex vector space with nondegenerate Hermitian form. If $\mathbb{F}$ is a field of characteristic different from $2$, then we give canonical matrices of isometric, selfadjoint, and skewadjoint operators on $V$ up to classification of symmetric and Hermitian forms over finite extensions of $\mathbb{F}$.

21 pages

References in corpus (5)

• Classification problems for system of forms and linear mappings
• Complexity of matrix problems
• Canonical matrices of bilinear and sesquilinear forms
• Canonical matrices of isometric operators on indefinite inner product spaces
• Classification of linear mappings between indefinite inner product spaces