Theorems · Inductive type · linear algebra
Module.DualBases
{R : Type u_1} →
{M : Type u_2} →
{ι : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (ι → M) → (ι → Module.Dual R M) → Prope and ε have characteristic properties of a basis and its dual
- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- AddCommMonoidstatement · cited by 12,281
- CommSemiringstatement · cited by 10,911
- Module.Dualstatement · cited by 583
Cited by19
Results whose statement or proof uses this declaration.
- Module.DualBases.basisstatement and proof · cited by 5
- Module.DualBases.coeffsstatement and proof · cited by 5
- Module.DualBases.dual_lcstatement and proof · cited by 3
- Module.DualBases.basis_repr_applystatement and proof · cited by 2
- Module.DualBases.eval_of_nestatement and proof · cited by 2
- Module.DualBases.eval_samestatement and proof · cited by 2
- Module.DualBases.coe_basisstatement and proof · cited by 1
- Module.DualBases.coeffs_applystatement and proof · cited by 1
- Module.DualBases.totalstatement and proof · cited by 1
- Module.DualBases.basis_repr_symm_applystatement and proof · cited by 0
- Module.DualBases.casesOnstatement and proof · cited by 0
- Module.DualBases.coe_dualBasisstatement and proof · cited by 0