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

Let V be a vector space over a field F with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If F=C, then we give canonical matrices of isometric and selfadjoint operators on V using known classifications of isometric and selfadjoint operators on a co...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2020-02, Vol.587, p.92-110
Main Authors: Caalim, Jonathan V., Futorny, Vyacheslav, Sergeichuk, Vladimir V., Tanaka, Yu-ichi
Format: Article
Language:English
Subjects:
H-unitary matrices
Indefinite inner product spaces
Isometric operators
Linear algebra
Matrices (mathematics)
Operators (mathematics)
Selfadjoint operators
Unitary operators
Vector space
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let V be a vector space over a field F with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If F=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 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 F.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.11.004