Theorems · Theorem · linear algebra
LinearMap.ker_toSpanSingleton
∀ (R : Type u_1) {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsDomain R]
[Module.IsTorsionFree R M] {x : M}, x ≠ 0 → (LinearMap.toSpanSingleton R M x).ker = ⊥- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- LinearMap.kerstatement · cited by 848
- Module.IsTorsionFreestatement and proof · cited by 600
- SetLike.extproof · cited by 92
- LinearMap.toSpanSingletonstatement · cited by 78
- smul_eq_zeroproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- isClosedEmbedding_smul_leftproof · cited by 5
- WittVector.isocrystal_classificationproof · cited by 0