Theorems · Theorem · linear algebra

LinearMap.BilinForm.nondegenerate_restrict_of_disjoint_orthogonal

∀ {R₁ : Type u_3} {M₁ : Type u_4} [inst : CommRing R₁] [inst_1 : AddCommGroup M₁] [inst_2 : Module R₁ M₁]
  (B : LinearMap.BilinForm R₁ M₁),
  B.IsRefl → ∀ {W : Submodule R₁ M₁}, Disjoint W (B.orthogonal W) → (B.restrict W).Nondegenerate

The restriction of a reflexive bilinear form B onto a submodule W is nondegenerate if Disjoint W (B.orthogonal W).

Defined in

Mathlib.LinearAlgebra.BilinearForm.Orthogonal

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule