matrix_mulVec — Mathlib

English

As above, the star operation on matrices is continuous.

Русский

Как и ранее, операция звезды над матрицами непрерывна.

LaTeX

$$$\\operatorname{ContinuousStar}(\\mathrm{M}_{m\\times m}(R)).$$$

Lean4

@[continuity, fun_prop]
theorem matrix_mulVec [NonUnitalNonAssocSemiring R] [ContinuousAdd R] [ContinuousMul R] [Fintype n]
    {A : X → Matrix m n R} {B : X → n → R} (hA : Continuous A) (hB : Continuous B) : Continuous fun x => A x *ᵥ B x :=
  continuous_pi fun i => ((continuous_apply i).comp hA).dotProduct hB

Похожие утверждения