Theorems · Theorem · linear algebra
Module.Dual.finrank_ker_add_one_of_ne_zero
∀ {K : Type u_1} {V₁ : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁]
{f : Module.Dual K V₁},
f ≠ 0 → ∀ [FiniteDimensional K V₁], Module.finrank K ↥(LinearMap.ker f) + 1 = Module.finrank K V₁- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientproof · cited by 2,301
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- add_commproof · cited by 1,535
- DivisionRingstatement and proof · cited by 1,062
- LinearMap.rangeproof · cited by 893
- LinearMap.kerstatement and proof · cited by 848
- Module.Dualstatement and proof · cited by 583
Cited by2
Results whose statement or proof uses this declaration.
- Module.Dual.isCompl_ker_of_disjoint_of_ne_botproof · cited by 2