DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

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 trace $tr (A)$ as the sum of the diagonal entries

Definition

For a square matrix $A = (a_{i j}) \in M_{n} (F)$ , its trace is the sum of its diagonal entries,

$tr (A) : = \sum_{i \in n} a_{i i} .$

For $n = 0$ , this is the empty sum, so the unique empty matrix has trace $0$ .

Depends on

Dependency tree · 2 levels

Sources

S. Axler, Linear Algebra Done Right, 4th ed., Definition 8.47