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

Autor(es)

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

Afiliação do(s) autor(es)

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

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

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

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 587, p. 92-110, FEB 15 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 18/24089-4 - Problemas de classificação para matrizes, espaços de matrizes e tensores
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático