Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-03
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.
Kernel and image of a linear map
Definition
For a linear map , its kernel and image are respectively
That both sets are linear subspaces, and that a trivial kernel characterises injectivity, is proved in The kernel and image are linear subspaces, and a linear map is injective if and only if its kernel is trivial ↗.