Canonical matrices of bilinear and sesquilinear forms
Abstract
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].
Keywords
Cite
@article{arxiv.0709.2408,
title = {Canonical matrices of bilinear and sesquilinear forms},
author = {Roger A. Horn and Vladimir V. Sergeichuk},
journal= {arXiv preprint arXiv:0709.2408},
year = {2007}
}
Comments
44 pages; misprints corrected; accepted for publication in Linear Algebra and its Applications (2007)