Witt's theorem is a basic result in the algebraic theory of quadratic forms, named after Ernst Witt. It states that any isometry between two subspaces of a nonsingular quadratic space over a field can be extended to an isometry of the whole space, with analogous statements holding for skew-symmetric, Hermitian, and skew-Hermitian bilinear forms. The theorem underlies the classification of quadratic forms and the definition of the Witt group of a field, which captures the stable theory of quadratic forms over that field, and it has further consequences for the structure and representation theory of isometry groups. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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1. Wikipedia: Witt's theorem
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The theorem applies to classification of quadratic forms over k and in particular allows one to define the Witt group W(k) which describes the "stable" theory of quadratic forms over the field k.
Witt's theorem (Wikipedia)
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