Theorems · Theorem · linear algebra
Finsupp.linearCombination_apply
∀ {α : Type u_1} {M : Type u_2} (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{v : α → M} (l : α →₀ R), (Finsupp.linearCombination R v) l = l.sum fun i a => a • v i- Cited by
- 38 results in Mathlib
- Foundations
- Depth 78 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- Finsupp.sumstatement · cited by 481
- Finsupp.linearCombinationstatement · cited by 269
Cited by38
Results whose statement or proof uses this declaration.
- Module.Basis.extproof · cited by 63
- Finsupp.range_linearCombinationproof · cited by 24
- Submodule.fg_of_fg_map_of_fg_inf_kerproof · cited by 7
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- Finsupp.span_image_eq_map_linearCombinationproof · cited by 7
- Module.Basis.ext'proof · cited by 6
- Module.Basis.mem_span_iff_repr_memproof · cited by 6
- IsBaseChange.basis_repr_comp_applyproof · cited by 3
- PowerBasis.aeval_minpolyGenproof · cited by 3
- LinearMap.IsOrthoᵢ.not_isOrtho_basis_self_of_separatingLeftproof · cited by 3
- Ideal.finsuppTotal_applyproof · cited by 2
- LinearEquiv.mem_dilatransvections_iff_rankproof · cited by 2