Theorems · Theorem · linear algebra
Subspace.finrank_add_finrank_dualCoannihilator_eq
∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
(W : Subspace K (Module.Dual K V)),
Module.finrank K ↥W + Module.finrank K ↥(Submodule.dualCoannihilator W) = Module.finrank K V- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Module.Dualstatement and proof · cited by 583
- Subspacestatement and proof · cited by 56
- Submodule.dualCoannihilatorstatement · cited by 41
- Subspace.dual_finrank_eqproof · cited by 5
- Subspace.finrank_add_finrank_dualAnnihilator_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.finrank_add_finrank_orthogonal'proof · cited by 2