Theorems · Theorem · linear algebra
Module.Basis.coe_repr_symm
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M), ↑b.repr.symm = Finsupp.linearCombination R ⇑b- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 82 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Finsuppstatement and proof · cited by 5,255
- Module.Basisstatement and proof · cited by 1,477
- LinearEquiv.symmstatement · cited by 1,461
- LinearEquiv.toLinearMapstatement · cited by 1,171
- LinearMap.extproof · cited by 844
- Module.Basis.reprstatement · cited by 498
Cited by7
Results whose statement or proof uses this declaration.
- Module.Basis.linearCombination_reprproof · cited by 26
- Module.Basis.repr_linearCombinationproof · cited by 6
- Algebra.IsSmoothAt.exists_notMem_isStandardSmoothproof · cited by 2
- Algebra.Presentation.differentials.comm₂₃'proof · cited by 1
- Basis.multilinearMap_applyproof · cited by 1
- Algebra.Generators.cotangentRestrict_bijective_of_isComplproof · cited by 1
- Algebra.Presentation.differentialsSolution_isPresentationproof · cited by 0