Theorems · Definition · geometry
AffineBasis.coord
{ι : Type u_1} →
{k : Type u_5} →
{V : Type u_6} →
{P : Type u_7} →
[inst : AddCommGroup V] →
[inst_1 : AddTorsor V P] → [inst_2 : Ring k] → [inst_3 : Module k V] → AffineBasis ι k P → ι → P →ᵃ[k] kThe ith barycentric coordinate of a point.
- Defined in
- Mathlib.LinearAlgebra.AffineSpace.Basis
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubproof · cited by 817
- AffineMapstatement · cited by 674
- AffineBasisstatement and proof · cited by 65
- AffineBasis.basisOfproof · cited by 11
- Module.Basis.sumCoordsproof · cited by 10
Cited by28
Results whose statement or proof uses this declaration.
- AffineBasis.toMatrixproof · cited by 11
- AffineBasis.coord_apply_combination_of_memstatement and proof · cited by 6
- AffineBasis.sum_coord_apply_eq_onestatement and proof · cited by 4
- AffineBasis.coord_applystatement and proof · cited by 4
- AffineBasis.coordsproof · cited by 4
- AffineBasis.affineCombination_coord_eq_selfstatement and proof · cited by 3
- AffineBasis.toMatrix_applystatement · cited by 2
- AffineBasis.toMatrix_vecMul_coordsproof · cited by 2
- continuous_barycentric_coordstatement and proof · cited by 2
- AffineBasis.surjective_coordstatement · cited by 1
- AffineBasis.affineIndependent_of_toMatrix_right_invproof · cited by 1
- AffineBasis.affineSpan_eq_top_of_toMatrix_left_invproof · cited by 1