Theorems · Theorem · linear algebra
Finsupp.linearCombination_unique
∀ {α : Type u_1} {M : Type u_2} (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Unique α] (l : α →₀ R) (v : α → M), (Finsupp.linearCombination R v) l = l default • v default- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Uniquestatement and proof · cited by 400
- Finsupp.linearCombinationstatement and proof · cited by 269
- Finsupp.linearCombination_singleproof · cited by 90
- Finsupp.unique_singleproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- linearIndependent_unique_iffproof · cited by 3
- rank_eq_zero_iffproof · cited by 3
- LinearIndependent.of_subsingleton'proof · cited by 2
- LinearMap.exists_eq_smul_id_of_forall_notLinearIndependentproof · cited by 1