Theorems · Theorem · linear algebra
Module.Basis.sum_dual_apply_smul_coord
∀ {R : Type uR} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M) [inst_3 : Fintype ι] (f : Module.Dual R M), ∑ x, f (b x) • b.coord x = f- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- Module.Basisstatement and proof · cited by 1,477
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