Theorems · Definition · linear algebra
Finsupp.lapply
{α : Type u_1} →
{M : Type u_2} →
{R : Type u_5} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → α → (α →₀ M) →ₗ[R] MInterpret fun f : α →₀ M ↦ f a as a linear map.
- Defined in
- Mathlib.LinearAlgebra.Finsupp.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Finsuppstatement and proof · cited by 5,255
- AddMonoidHomproof · cited by 3,230
- ZeroHom.toFunproof · cited by 101
- AddMonoidHom.toZeroHomproof · cited by 61
- Finsupp.applyAddHomproof · cited by 3
Cited by21
Results whose statement or proof uses this declaration.
- Module.Basis.coordproof · cited by 64
- linearIndependent_iff'ₛproof · cited by 9
- KaehlerDifferential.mvPolynomialBasis_repr_applyproof · cited by 2
- Module.Basis.repr_apply_eqproof · cited by 2
- Finsupp.lapply_applystatement · cited by 2
- ModuleCat.FreeMonoidal.εIsoproof · cited by 2
- LinearMap.finsuppLinearMap_bijective_of_finiteproof · cited by 1
- LinearMap.finsuppLinearMap_bijective_of_moduleFiniteproof · cited by 1
- Finsupp.iInf_ker_lapply_le_botstatement and proof · cited by 1
- Finsupp.lsingle_range_le_ker_lapplystatement and proof · cited by 1
- Finsupp.lapply_comp_lsingle_of_nestatement · cited by 1
- Finsupp.lapply_comp_lsingle_samestatement · cited by 1