`BookProof.ChapterH7.reduceGenerator_isHermitian` (m : ℕ) (V : EuclideanSpace ℂ (Fin m) →L[ℂ] E) (X : E →L[ℂ] E) (hX : IsSelfAdjoint X) : (reduceGenerator m V X).IsHermitian

Proved

BookProof.ChapterH7.reduceGenerator_isHermitian

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterH7.

BookProof.ChapterH7.reduceGenerator_isHermitian (m : ℕ) (V : EuclideanSpace ℂ (Fin m) →L[ℂ] E) (X : E →L[ℂ] E) (hX : IsSelfAdjoint X) : (reduceGenerator m V X).IsHermitian

Formalization note: Lean 4 identifier BookProof.ChapterH7.reduceGenerator_isHermitian.

Preamble

-- Generated from ChapterH7.lean — theorem BookProof.ChapterH7.reduceGenerator_isHermitian
import Definitions.Def_ChapterH4
import Mathlib
import Definitions.Def_ChapterH7
import Definitions.Def_ChapterH6
open BookProof.ChapterH6
open BookProof.ChapterH7


noncomputable section

open BookProof.ChapterH4 BookProof.ChapterH6

variable {E F : Type*}
  [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
  [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]

Formal statement

theorem BookProof.ChapterH7.reduceGenerator_isHermitian (m : ℕ) (V : EuclideanSpace ℂ (Fin m) →L[ℂ] E)
    (X : E →L[ℂ] E) (hX : IsSelfAdjoint X) :
    (reduceGenerator m V X).IsHermitian := by sorry

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