DefinitionDefinition: 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.

Linear map between vector spaces over the same field

Let $V$ and $W$ be vector spaces over the same field $F$ . A function $T : V \to W$ is linear when

$T (a u + b v) = a T (u) + b T (v)$

for all $a, b \in F$ and $u, v \in V$ . Such a function is a linear map, or linear transformation.

Depends on