✦ LIBER ✦

Bilinear forms over an algebraically closed field

✍ Scribed by B. Corbas; G.D. Williams

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 124 KB
Volume: 165
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00123-2

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✦ Synopsis

The general structure theory of bilinear forms, as formulated by Riehm and Scharlau, is here applied over an algebraically closed ÿeld of characteristic = 2 to produce explicit representatives for the equivalence classes of forms, or, what is the same, for congruence classes of (n × n) matrices.

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The purpose of this paper is to obtain a complete set of matrix representatives for the bilinear forms on a three-dimensional vector space over a finite field of any characteristic, without assuming that the form is symmetric or non-degenerate. (~