Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-13
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Bilinear forms, and symmetric, skew-symmetric, and alternating bilinear forms

Definition

Let V be a vector space over F. A bilinear form on V is a function B:V×V→F that is linear in each variable separately.

The form is

  • symmetric when B(u,v)=B(v,u) for all u,v∈V;
  • skew-symmetric when B(u,v)=−B(v,u) for all u,v∈V;
  • alternating when B(v,v)=0 for every v∈V.

These conditions are kept distinct because their relations depend on the characteristic of F.

Depends on

Dependency tree · 2 levels

Sources