Theorems · Theorem · linear algebra

LinearMap.BilinForm.finrank_add_finrank_orthogonal

∀ {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},
  B.IsRefl →
    ∀ (W : Submodule K V),
      Module.finrank K ↥W + Module.finrank K ↥(B.orthogonal W) =
        Module.finrank K V + Module.finrank K ↥(W ⊓ B.orthogonal ⊤)

Defined in

Mathlib.LinearAlgebra.BilinearForm.Orthogonal

Cited by

2 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional