Alphabeta Math
DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generated
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.

Equivalent complex norms

Definition

Let M and N be complex norms (Complex norm and complex normed space) on the same complex vector space V. They are equivalent complex norms if there are positive real constants c,C∈R such that

cM(v)≤N(v)≤CM(v)for every v∈V.

Both inequalities and the positivity of c,C are in the real complete ordered field (Complete ordered field (least-upper-bound property), with completeness established in The Cauchy-sequence reals have the least-upper-bound property); the vector scalar field remains C. No order comparison of complex numbers is intended.

Depends on

Used by

Dependency tree · two levels

13 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources