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

The canonical evaluation map $J_{V} : V \to V^{* *}$ given by $J_{V} (v) (f) = f (v)$

Definition

For a vector space $V$ , write $V^{* *} : = (V^{*})^{*}$ . The canonical evaluation map into the double dual is

$J_{V} : V ⟶ V^{* *}, J_{V} (v) (f) : = f (v) .$

For fixed $v$ , evaluation at $v$ is linear in $f$ , so $J_{V} (v) \in V^{* *}$ . The construction uses no basis and is therefore canonical.

Depends on

Linear functionals and the algebraic dual $V^*=\mathcal L(V,F)$

Used by

Assuming choice, the canonical map J_V:V→ V^** is linear and injective Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 5 results over 5 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

H. Pinkham, Linear Algebra, §6.1 (standard reference, not scraped)
K. Conrad, Infinite-Dimensional Dual Spaces (standard reference, not scraped)

The canonical evaluation map JV:V→V∗∗JV​:V→V∗∗ given by JV(v)(f)=f(v)JV​(v)(f)=f(v)