DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-09-01

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.

A type $(r, s)$ tensor on a finite-dimensional vector space

Definition

Let $V$ be a finite-dimensional real vector space, and let $r, s \geq 0$ . A type $(r, s)$ tensor on $V$ is a multilinear map

$T : (V^{*})^{r} \times V^{s} \to R .$

With this convention, vectors are type $(1, 0)$ tensors and covectors are type $(0, 1)$ tensors.

Depends on

Dependency tree · 2 levels

Sources