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`BookProof.ChapterWeakValue.ip_projMat` (a : Fin n) (f v : Fin n → ℂ) : ip f (projMat a *ᵥ v) = starRingEnd ℂ (f a) * v a

Proved
BookProof.ChapterWeakValue.ip_projMat

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.ip_projMat (a : Fin n) (f v : Fin n → ℂ) : ip f (projMat a *ᵥ v) = starRingEnd ℂ (f a) * v a

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

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


open scoped BigOperators Matrix


variable {n : ℕ}
Formal statement
theorem BookProof.ChapterWeakValue.ip_projMat (a : Fin n) (f v : Fin n → ℂ) :
    ip f (projMat a *ᵥ v) = starRingEnd ℂ (f a) * v a := by sorry

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