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

Author(s)

Caalim, V, Jonathan ; Futorny, Vyacheslav ^[1] ; Sergeichuk, Vladimir V. ^[2] ; Tanaka, Yu-ichi ^[3]

Affiliation

^[1] Univ Sao Paulo, Dept Math, Sao Paulo - Brazil

^[2] Inst Math, Tereshchenkivska 3, Kiev - Ukraine

^[3] Joso Gakuin High Sch, Tsuchiura, Ibaraki - Japan

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 587, p. 92-110, FEB 15 2020.
• Web of Science Citations: 0

Abstract

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. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/24089-4 - Classification problems for matrices, matrix spaces and tensors
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants