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.

Invertible Euclidean linear maps

Let $n \geq 1$ . A linear map $A : R^{n} \to R^{n}$ (A linear map $L : R^{m} \to R^{n}$ in Euclidean coordinates) is invertible when there is a linear map $B : R^{n} \to R^{n}$ such that

$B (A u) = u and A (B u) = u (u \in R^{n}) .$

The map $B$ is unique: if $C$ has the same two properties, then $C = C \circ (A \circ B) = (C \circ A) \circ B = B$ . It is denoted $A^{- 1}$ .

Depends on