Theorems · Theorem · linear algebra
LinearIndependent.fintypeLinearCombination_injective
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : Fintype ι],
LinearIndependent R v → Function.Injective ⇑(Fintype.linearCombination R v)Alias of the forward direction of linearIndependent_iff_injective_fintypeLinearCombination.
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- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- Fintypestatement and proof · cited by 7,736
- LinearIndependentstatement · cited by 560
- Fintype.linearCombinationstatement · cited by 26
- linearIndependent_iff_injective_fintypeLinearCombinationproof · cited by 3
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