`BookProof.ChapterSternGerlach.exists_uniform_unitary` (n : ℕ) (hn : 0 < n) : ∃ U ∈ Matrix.unitaryGroup (Fin n) ℂ, ∀ i j : Fin n, Complex.normSq (U i j) = 1 / n

Proved

BookProof.ChapterSternGerlach.exists_uniform_unitary

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSternGerlach.

BookProof.ChapterSternGerlach.exists_uniform_unitary (n : ℕ) (hn : 0 < n) : ∃ U ∈ Matrix.unitaryGroup (Fin n) ℂ, ∀ i j : Fin n, Complex.normSq (U i j) = 1 / n

Formalization note: Lean 4 identifier BookProof.ChapterSternGerlach.exists_uniform_unitary.

Preamble

-- Generated from ChapterSternGerlach.lean — theorem BookProof.ChapterSternGerlach.exists_uniform_unitary
import Mathlib
import Definitions.Def_ChapterSternGerlach
open BookProof.ChapterSternGerlach



open Complex Matrix Finset

Formal statement

theorem BookProof.ChapterSternGerlach.exists_uniform_unitary (n : ℕ) (hn : 0 < n) :
    ∃ U ∈ Matrix.unitaryGroup (Fin n) ℂ,
      ∀ i j : Fin n, Complex.normSq (U i j) = 1 / n := by sorry

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