SeparatingRight — Mathlib

English

Permuting the indices of a symmetric tensor product by a permutation does not change the tensor.

Русский

Перестановка индексов в симметрическом тензорном произведении не изменяет тензор.

LaTeX

$$(⨂ₛ[R] i, f (e i)) = ⨂ₛ[R] i, f i$$

Lean4

/-- A bilinear map is called right-separating if
the only element that is right-orthogonal to every other element is `0`; i.e.,
for every nonzero `y` in `M₂`, there exists `x` in `M₁` with `B x y ≠ 0`. -/
def SeparatingRight (B : M₁ →ₛₗ[I₁] M₂ →ₛₗ[I₂] M) : Prop :=
  ∀ y : M₂, (∀ x : M₁, B x y = 0) → y = 0

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