Theorems · Theorem · linear algebra

LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate

∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
  {B : LinearMap.BilinForm K V} {W : Submodule K V},
  B.IsRefl → (B.restrict W).Nondegenerate → IsCompl W (B.orthogonal W)

A subspace is complement to its orthogonal complement with respect to some reflexive bilinear form if that bilinear form restricted on to the subspace is nondegenerate.

Defined in

Mathlib.LinearAlgebra.BilinearForm.Orthogonal

Cited by

3 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional