Prove2Me

`BookProof.ChapterWeakValue.ip_conj_mulVec` (A : Matrix (Fin n) (Fin n) ℂ) (f v : Fin n → ℂ) : starRingEnd ℂ (ip f (A *ᵥ v)) = ip v (Aᴴ *ᵥ f)

Proved
BookProof.ChapterWeakValue.ip_conj_mulVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.ip_conj_mulVec (A : Matrix (Fin n) (Fin n) ℂ) (f v : Fin n → ℂ) : starRingEnd ℂ (ip f (A *ᵥ v)) = ip v (Aᴴ *ᵥ f)

Formalization note: Lean 4 identifier BookProof.ChapterWeakValue.ip_conj_mulVec.

Preamble
-- Generated from ChapterWeakValue.lean — theorem BookProof.ChapterWeakValue.ip_conj_mulVec
import Mathlib
import Definitions.Def_ChapterWeakValue
open BookProof.ChapterWeakValue


open scoped BigOperators Matrix


variable {n : ℕ}
Formal statement
theorem BookProof.ChapterWeakValue.ip_conj_mulVec (A : Matrix (Fin n) (Fin n) ℂ) (f v : Fin n → ℂ) :
    starRingEnd ℂ (ip f (A *ᵥ v)) = ip v (Aᴴ *ᵥ f) := by sorry

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