`BookProof.ChapterCollapseDiagonal.trace_diagonal_mul` (ρ O : Matrix (Fin n) (Fin n) ℂ) (hρ : IsDiagonal ρ) : (ρ * O).trace = ∑ i, ρ i i * O i i

Proved

BookProof.ChapterCollapseDiagonal.trace_diagonal_mul

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCollapseDiagonal.

BookProof.ChapterCollapseDiagonal.trace_diagonal_mul (ρ O : Matrix (Fin n) (Fin n) ℂ) (hρ : IsDiagonal ρ) : (ρ * O).trace = ∑ i, ρ i i * O i i

Formalization note: Lean 4 identifier BookProof.ChapterCollapseDiagonal.trace_diagonal_mul.

Preamble

-- Generated from ChapterCollapseDiagonal.lean — theorem BookProof.ChapterCollapseDiagonal.trace_diagonal_mul
import Mathlib
import Definitions.Def_ChapterCollapseDiagonal
open BookProof.ChapterCollapseDiagonal


open scoped BigOperators
open Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterCollapseDiagonal.trace_diagonal_mul (ρ O : Matrix (Fin n) (Fin n) ℂ) (hρ : IsDiagonal ρ) :
    (ρ * O).trace = ∑ i, ρ i i * O i i := by sorry

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