Theorems · Theorem · linear algebra

Subspace.isCompl_dualAnnihilator

∀ {K : Type u_1} {V₁ : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁]
  {W W' : Subspace K V₁}, IsCompl W W' → IsCompl (Submodule.dualAnnihilator W) (Submodule.dualAnnihilator W')

For vector spaces, dual annihilators carry direct sum decompositions to direct sum decompositions.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModule