weightedVSub_mem_vectorSpan
∀ {ι : Type u_1} {k : Type u_2} {V : Type u_3} {P : Type u_4} [inst : Ring k] [inst_1 : AddCommGroup V]
[inst_2 : Module k V] [inst_3 : AddTorsor V P] {s : Finset ι} {w : ι → k},
∑ i ∈ s, w i = 0 → ∀ (p : ι → P), (s.weightedVSub p) w ∈ vectorSpan k (Set.range p)A weightedVSub with sum of weights 0 is in the vectorSpan of
an indexed family.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Finsuppproof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
Cited by2
Results whose statement or proof uses this declaration.
- affineCombination_mem_affineSpanproof · cited by 12
- mem_vectorSpan_iff_eq_weightedVSubproof · cited by 1