updateRow_subsingleton — Mathlib

English

For Mul α, AddCommMonoid α and Unique ι, vecMulVec w v = replicateCol ι w * replicateRow ι v.

Русский

Для Mul α, AddCommMonoid α и Unique ι: vecMulVec w v = replicateCol ι w * replicateRow ι v.

LaTeX

$$$ vecMulVec\ w\ v = replicateCol\ ι\ w * replicateRow\ ι\ v $$$

Lean4

@[simp]
theorem updateRow_subsingleton [Subsingleton m] (A : Matrix m n R) (i : m) (b : n → R) :
    A.updateRow i b = (replicateRow (Fin 1) b).submatrix (Function.const m 0) id :=
  by
  ext x y
  simp [Subsingleton.elim i x]

Похожие утверждения