DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-13

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.

Polynomial evaluation at an endomorphism: $p (T) = \sum_{k} a_{k} T^{k}$

Definition

Let $T : V \to V$ be an endomorphism and let $p (x) = \sum_{k \geq 0} a_{k} x^{k} \in F [x]$ . Define

$p (T) : = \sum_{k \geq 0} a_{k} T^{k} \in L (V, V),$

where $T^{0} : = I_{V}$ and $T^{k + 1} : = T \circ T^{k}$ . The sum is finite because the coefficient sequence of $p$ has finite support. In particular, the zero polynomial evaluates to the zero endomorphism and the constant polynomial $1$ evaluates to $I_{V}$ .

Polynomial evaluation at an endomorphism: $p (T) = \sum_{k} a_{k} T^{k}$

Definition

Depends on

Dependency tree · 2 levels

Sources

Polynomial evaluation at an endomorphism: p(T)=∑kakTkp(T)=∑k​ak​Tk

Definition

Depends on

Dependency tree · 2 levels

Sources

Polynomial evaluation at an endomorphism: $p (T) = \sum_{k} a_{k} T^{k}$