Balanced — Mathlib

English

The matrix representation of innerSL with bases b and b₂ is equal to vecMulVec(star b₂)(star (b.repr x)).

Русский

Матрица отображения innerSL относительно оснований b и b₂ равна vecMulVec(звёздочка b₂)(звёздочка (b.repr x)).

LaTeX

$$$(innerSL\\ {\\mathbb{k}}\\ x)_{b b_2} = \\mathrm{vecMulVec}(\\star b_2)(\\star (b.repr\\ x)).$$$

Lean4

/-- A set `A` is balanced if `a • A` is contained in `A` whenever `a` has norm at most `1`. -/
def Balanced (A : Set E) :=
  ∀ a : 𝕜, ‖a‖ ≤ 1 → a • A ⊆ A

Похожие утверждения