blockDiag'_apply — Mathlib

English

Taking the transpose commutes with block diagonalization blockDiag': (blockDiag' M)ᵀ = blockDiag' (Mᵀ) and evaluated blockwise.

Русский

Транспонирование commuting с блочно-диагонализацией: (blockDiag' M)ᵀ = blockDiag' (Mᵀ).

LaTeX

$$$ \\mathrm{blockDiag}' M^{\\top} k = (\\mathrm{blockDiag}' M k)^{\\top} $$$

Lean4

theorem blockDiag'_apply (M : Matrix (Σ i, m' i) (Σ i, n' i) α) (k : o) (i j) : blockDiag' M k i j = M ⟨k, i⟩ ⟨k, j⟩ :=
  rfl

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