On Witt's Theorem for Nonalternating Symmetric Bilinear Forms Over a Field of Characteristic 2 PDF Download

Author: Vera Pless
Publisher:
ISBN:
Category : Bilinear forms
Languages : en
Pages : 18

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Book Description
The purpose of this note Is to show that an analogue to Witt's theorem holds for a non-degenerate, non-alternating, symmetric bilinear form f over a field K of characteristic 2 where f(x, x) takes its values in a subfield K* such that K contains the square root of any element in K*. As is known, [2, p. 171] Witt's theorem does not hold in general for a field of characteristic 2. However, the following shows that an isometry of subspace can be extended if it leaves a certain unique vector invariant. The invariants of a subspace of V with respect to the orthogonal group are determined.