complexBasis — Mathlib

English

For each x ∈ ZMod n, zmodAddEquiv x equals circleEquivComplex (zmod n x).

Русский

Для каждого x ∈ ℤ/nℤ zmodAddEquiv x равно circleEquivComplex (zmod n x).

LaTeX

$$$ zmodAddEquiv x = circleEquivComplex (zmod n x) $$$

Lean4

/-- Complex-valued characters of a finite abelian group `α` form a basis of `α → ℂ`. -/
def complexBasis : Basis (AddChar α ℂ) ℂ (α → ℂ) :=
  basisOfLinearIndependentOfCardEqFinrank (AddChar.linearIndependent _ _) <| by cases nonempty_fintype α;
    rw [card_eq, Module.finrank_fintype_fun_eq_card]

Похожие утверждения