Theorems · Definition · linear algebra
Module.DualBases.coeffs
{R : Type u_1} →
{M : Type u_2} →
{ι : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] →
[inst_2 : Module R M] → {e : ι → M} → {ε : ι → Module.Dual R M} → Module.DualBases e ε → M → ι →₀ RThe coefficients of v on the basis e
- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Module.Dualstatement and proof · cited by 583
- Set.Finite.toFinsetproof · cited by 351
- Module.DualBasesstatement and proof · cited by 15
- Module.DualBases.finiteproof · cited by 0
Cited by6
Results whose statement or proof uses this declaration.
- Module.DualBases.basisproof · cited by 5
- Module.DualBases.basis_repr_applystatement · cited by 2
- Module.DualBases.coeffs_applystatement · cited by 1
- Module.DualBases.coeffs.congr_simpstatement and proof · cited by 0
- Module.DualBases.coeffs_lcstatement · cited by 0
- Module.DualBases.lc_coeffsstatement and proof · cited by 0