Canonical matrices of bilinear and sesquilinear forms

Details Canonical matrices of bilinear and sesquilinear forms Canonical matrices of bilinear and sesquilinear forms

2007-09-15

arxiv.org/abs/0709.2408v2

Linear Algebra Appl. 428 (2008) 193-223

Mathematics

Representation Theory

44 pages; misprints corrected; accepted for publication in Linear Algebra and its Applications (2007)

Scientific paper

10.1016/j.laa.2007.07.023

Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of F. A method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices. This method has its origins in representation theory and was devised in [V.V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501].

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