Theorems · Theorem · linear algebra
Finsupp.span_eq_range_linearCombination
∀ {M : Type u_2} (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (s : Set M),
Submodule.span R s = (Finsupp.linearCombination R Subtype.val).rangeA version of Finsupp.range_linearCombination which is useful for going in the other
direction
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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
- Submodulestatement and proof · cited by 7,192
- Finsuppstatement · cited by 5,255
- Submodule.spanstatement and proof · cited by 1,504
- LinearMap.rangestatement · cited by 893
- Finsupp.linearCombinationstatement · cited by 269
- Subtype.range_coe_subtypeproof · cited by 170
- Finsupp.range_linearCombinationproof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- rank_span_leproof · cited by 9
- Finsupp.mem_span_iff_linearCombinationproof · cited by 7
- Ideal.homogeneous_spanproof · cited by 1