Theorems · Theorem · linear algebra
Module.Basis.toDual_apply_left
∀ {R : Type uR} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : DecidableEq ι] (b : Module.Basis ι R M) (m : M) (i : ι), (b.toDual m) (b i) = (b.repr m) i- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- 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
- Finsuppstatement · cited by 5,255
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Module.Dualstatement · cited by 583
- Module.Basis.reprstatement and proof · cited by 498
- Module.Basis.linearCombination_reprproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- Module.Basis.toDual_toDualproof · cited by 1
- Module.Basis.toDual_eq_reprproof · cited by 1