Theorems · Definition · linear algebra
LinearIndepOn
{ι : Type u'} →
(R : Type u_2) →
{M : Type u_4} → (ι → M) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Set ι → PropLinearIndepOn R v s states that the vectors in the family v that are indexed
by the elements of s are linearly independent over R.
- Cited by
- 211 results in Mathlib
- Foundations
- Depth 79 from the axioms, rests on 1,818 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemproof · cited by 7,166
- LinearIndependentproof · cited by 560
Cited by225
Results whose statement or proof uses this declaration.
- LinearIndepOn.extendstatement and proof · cited by 28
- Module.rank_lt_aleph0proof · cited by 23
- Module.Basis.mk_eq_rank''proof · cited by 23
- Module.rank_defstatement and proof · cited by 21
- rank_subsingletonproof · cited by 19
- Submodule.eq_top_of_finrank_eqproof · cited by 15
- LinearIndepOn.monostatement and proof · cited by 14
- LinearIndependent.linearIndepOn_idstatement · cited by 14
- rank_subsingleton'proof · cited by 13
- LinearIndependent.pair_iffproof · cited by 10
- IsProperLinearSetproof · cited by 9
- Module.Basis.extendstatement and proof · cited by 9
Showing the 200 most cited of 225.