`BookProof.DensitySpectral.bornKernel_col_sum` (U : Matrix.unitaryGroup n ℂ) (j : n) : ∑ i, bornKernel (U : Matrix n n ℂ) i j = 1

Proved

BookProof.DensitySpectral.bornKernel_col_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDensityMarginalConditional.

BookProof.DensitySpectral.bornKernel_col_sum (U : Matrix.unitaryGroup n ℂ) (j : n) : ∑ i, bornKernel (U : Matrix n n ℂ) i j = 1

Formalization note: Lean 4 identifier BookProof.DensitySpectral.bornKernel_col_sum.

Preamble

-- Generated from ChapterDensityMarginalConditional.lean — theorem BookProof.DensitySpectral.bornKernel_col_sum
import Mathlib
import Definitions.Def_ChapterDensityMarginalConditional
open BookProof.DensitySpectral



open Matrix
open scoped BigOperators ComplexOrder

variable {n : Type*} [Fintype n] [DecidableEq n]

Formal statement

theorem BookProof.DensitySpectral.bornKernel_col_sum (U : Matrix.unitaryGroup n ℂ) (j : n) :
    ∑ i, bornKernel (U : Matrix n n ℂ) i j = 1 := by sorry

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