`BookProof.ChapterA.conjCLM_unitScale` (α : V ≃ₗᵢ[ℂ] W) (l : ℂ) (hl : ‖l‖ = 1) (m : V →L[ℂ] V) : conjCLM (α.trans (unitScaleEquiv l hl)) m = conjCLM α m

Proved

BookProof.ChapterA.conjCLM_unitScale

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2d.

BookProof.ChapterA.conjCLM_unitScale (α : V ≃ₗᵢ[ℂ] W) (l : ℂ) (hl : ‖l‖ = 1) (m : V →L[ℂ] V) : conjCLM (α.trans (unitScaleEquiv l hl)) m = conjCLM α m

Formalization note: Lean 4 identifier BookProof.ChapterA.conjCLM_unitScale.

Preamble

-- Generated from ChapterA2d.lean — theorem BookProof.ChapterA.conjCLM_unitScale
import Mathlib
import Definitions.Def_ChapterA2d
import Definitions.Def_ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℂ W] [CompleteSpace W]

Formal statement

theorem BookProof.ChapterA.conjCLM_unitScale (α : V ≃ₗᵢ[ℂ] W) (l : ℂ) (hl : ‖l‖ = 1) (m : V →L[ℂ] V) :
    conjCLM (α.trans (unitScaleEquiv l hl)) m = conjCLM α m := by sorry

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