Theorems · Definition · group theory
AddChar.complexBasis
(α : Type u_1) → [inst : AddCommGroup α] → [Finite α] → Module.Basis (AddChar α ℂ) ℂ (α → ℂ)
Complex-valued characters of a finite abelian group α form a basis of α → ℂ.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Complexstatement and proof · cited by 5,565
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement · cited by 1,477
- AddCharstatement · cited by 286
- basisOfLinearIndependentOfCardEqFinrankproof · cited by 3
- AddChar.linearIndependentproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- AddChar.complexBasis_applystatement · cited by 1
- AddChar.exists_apply_ne_zeroproof · cited by 1
- AddChar.coe_complexBasisstatement · cited by 1
- AddChar.complexBasis.congr_simpstatement and proof · cited by 0