Theorems · Theorem · linear algebra
Module.Basis.coe_dualBasis
∀ {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) [inst_4 : Finite ι], ⇑b.dualBasis = b.coord- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.extproof · cited by 844
- Module.Dualstatement · cited by 583
- Module.Basis.coordstatement · cited by 64
- Module.Basis.dualBasisstatement · cited by 29
- Module.Basis.dualBasis_applyproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.apply_dualBasis_leftproof · cited by 5
- TensorProduct.dualDistribInvOfBasis_applyproof · cited by 3
- PiTensorProduct.dualDistribInvOfBasis_applyproof · cited by 2
- LinearMap.trace_eq_contract_of_basisproof · cited by 2
- Module.Basis.toDual_toDualproof · cited by 1
- Module.Free.bijective_algebraMap_of_finrank_eq_oneproof · cited by 1
- TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverseproof · cited by 0
- TensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverseproof · cited by 0
- contractLeft_assoc_coevaluationproof · cited by 0
- Module.Basis.flag_le_ker_dualproof · cited by 0
- Module.Basis.linearCombination_coordproof · cited by 0
- TensorProduct.dualDistribEquivOfBasis_symm_applyproof · cited by 0