blockDiag_sub — Mathlib

English

BlockDiag is submatrix-compatible: (blockDiagonal' M).submatrix equals blockDiagonal M.

Русский

BlockDiagonal' сохраняет подматрицу: (blockDiagonal' M).submatrix = blockDiagonal M.

LaTeX

$$$ (blockDiagonal' M).submatrix (Prod.toSigma \circ Prod.swap) (Prod.toSigma \circ Prod.swap) = blockDiagonal M $$$

Lean4

@[simp]
theorem blockDiag_sub [AddGroup α] (M N : Matrix (m × o) (n × o) α) : blockDiag (M - N) = blockDiag M - blockDiag N :=
  map_sub (blockDiagAddMonoidHom m n o α) M N

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