Alphabeta MathHow 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.
Simultaneous diagonalisability: one basis that diagonalises every endomorphism in a family
Definition
A family of endomorphisms of a finite-dimensional vector space is simultaneously diagonalisable if there is one ordered basis of in which the matrix of every is diagonal. Equivalently, has a basis consisting of vectors that are eigenvectors for every member of , matching the one-operator definition in A diagonalisable endomorphism is one admitting a basis of eigenvectors, equivalently a diagonal matrix representation.
The empty family is simultaneously diagonalisable in every finite-dimensional space: any ordered basis works. On the zero space the empty ordered basis works for every family.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 20 results over 10 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
- Keith Conrad, The Minimal Polynomial and Some Applications, §5 (standard reference, not scraped)