Theorems · Definition · linear algebra
Module.DualBases.lc
{R : Type u_1} →
{M : Type u_2} →
[inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → {ι : Type u_4} → (ι → M) → (ι →₀ R) → Mlinear combinations of elements of e.
This is a convenient abbreviation for Finsupp.linearCombination R e l
- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finsupp.sumproof · cited by 481
Cited by6
Results whose statement or proof uses this declaration.
- Module.DualBases.basisproof · cited by 5
- Module.DualBases.dual_lcstatement · cited by 3
- Module.DualBases.lc_defstatement · cited by 1
- Module.DualBases.basis_repr_symm_applystatement · cited by 0
- Module.DualBases.coeffs_lcstatement and proof · cited by 0
- Module.DualBases.lc_coeffsstatement · cited by 0