kronecker_ofNat — Mathlib

English

For a non-associative semiring α and a at least two, (ofNat a) ⊗ₖ B equals a blockDiagonal scaling of B with (ofNat a).

Русский

Для неассоциируемого полугруппового кольца, при a ≥ 2, (ofNat a) ⊗ₖ B равно блочно-дiагональной нормализации с a.

LaTeX

$$$ (\operatorname{ofNat}(a) : Matrix l l α) \otimes_k B = \operatorname{reindex} (\operatorname{prodComm} _) (\operatorname{prodComm} _) ( \operatorname{blockDiagonal} (\lambda _, (\operatorname{ofNat}(a) : α) \cdot B ) ) $$$

Lean4

theorem kronecker_ofNat [NonAssocSemiring α] [DecidableEq n] (A : Matrix l m α) (b : ℕ) [b.AtLeastTwo] :
    A ⊗ₖ (ofNat(b) : Matrix n n α) = blockDiagonal fun _ => A <• (ofNat(b) : α) :=
  kronecker_diagonal _ _

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