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Results tagged with quadratic-forms
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user 12858
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
8
votes
quadratic forms over fields of characteristic 2
The Algebraic and Geometric Theory of Quadratic Forms by Elman, Karpenko and Merkurjev is a standard recent reference for the theory of quadratic forms, paying special attention to the differences bet …
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2
votes
Orthogonal transformations fixing a subspace (setwise)
The full orthogonal group $O(Q)$ is generated by reflections, i.e. involutory isometries fixing a hyperplane pointwise:
$$\pi_v : V \to V : x \mapsto x - \frac{Q(v,x)}{Q(v)} v,$$
where $v$ is an aniso …
- 6,614
2
votes
Quadratic forms question
Here is one way to do it. Assume that (4) holds for all $a,b \in F^\times$, and now let $a \in F^\times$ be arbitrary. If $\langle 1,a \rangle$ is isotropic, then it is of course universal, so we may …
- 6,614
1
vote
Generators of the orthogonal group of a quadratic form in odd dimension in characteristic 2
For a reference, you could use Theorem I.5.1 from C. Chevalley, The Algebraic Theory of Spinors, Columbia University Press, New York, 1954. (This also appears in volume 2 of his collected works.) The …
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