Roger A. Horn, Vladimir V. Sergeichuk
Published 2007-09-15, updated 2007-10-03Version 2
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].
Comments: 44 pages; misprints corrected; accepted for publication in Linear Algebra and its Applications (2007)
Journal: Linear Algebra Appl. 428 (2008) 193-223
A regularization algorithm for matrices of bilinear and sesquilinear forms
Classification problems for system of forms and linear mappings
Classification of sesquilinear forms with the first argument on a subspace or a factor space
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