Theorems · Definition · linear algebra
LinearMap.toSpanSingleton
(R : Type u_1) → (M : Type u_4) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → M → R →ₗ[R] M
Given an element x of a module M over R, the natural map from
R to scalar multiples of x. See also LinearMap.ringLmapEquivSelf.
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearMapstatement · cited by 10,215
- LinearMap.idproof · cited by 625
- LinearMap.smulRightproof · cited by 54
Cited by92
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.toSpanSingletonproof · cited by 133
- LinearMap.toSpanSingleton_applystatement and proof · cited by 38
- RootPairing.Polarizationproof · cited by 20
- Ideal.torsionOfproof · cited by 14
- RootPairing.PolarizationInproof · cited by 12
- LinearEquiv.toSpanNonzeroSingletonproof · cited by 10
- CliffordAlgebraComplex.toComplexproof · cited by 8
- RootPairing.Polarization_applyproof · cited by 8
- Complex.liftAuxproof · cited by 7
- LinearIsometry.toSpanSingletonproof · cited by 6
- LinearMap.span_singleton_eq_rangestatement · cited by 6
- Polynomial.mkDerivationproof · cited by 5