DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

Nilpotent endomorphisms and their nilpotency index

Definition

An endomorphism $N : V \to V$ is nilpotent if $N^{k} = 0$ for some positive integer $k$ . Its nilpotency index is the least positive integer $r$ such that $N^{r} = 0$ ; this least exponent exists by the well-ordering principle (The well-ordering principle).

The unique endomorphism of the zero space is nilpotent. With the same least-positive-exponent convention, its nilpotency index is $1$ because its identity and zero endomorphisms coincide.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 29 results over 9 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

S. Axler, Linear Algebra Done Right, 4th ed., Section 8B (standard reference, not scraped)