Theorems · Inductive type · geometry
AffineBasis
Type u₁ →
(k : Type u₂) →
{V : Type u₃} →
(P : Type u₄) → [inst : AddCommGroup V] → [AddTorsor V P] → [inst_2 : Ring k] → [Module k V] → Type (max u₁ u₄)An affine basis is a family of affine-independent points whose span is the top subspace.
- Defined in
- Mathlib.LinearAlgebra.AffineSpace.Basis
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 6 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
- AddCommGroupstatement · cited by 12,871
- Ringstatement · cited by 7,463
- AddTorsorstatement · cited by 1,657
Cited by77
Results whose statement or proof uses this declaration.
- AffineBasis.coordstatement and proof · cited by 26
- AffineBasis.toMatrixstatement and proof · cited by 11
- AffineBasis.basisOfstatement and proof · cited by 11
- AffineBasis.totstatement and proof · cited by 8
- AffineBasis.reindexstatement and proof · cited by 7
- AffineBasis.coord_apply_combination_of_memstatement and proof · cited by 6
- AffineBasis.sum_coord_apply_eq_onestatement and proof · cited by 4
- AffineBasis.basisOf_applystatement and proof · cited by 4
- AffineBasis.coord_applystatement and proof · cited by 4
- AffineBasis.coordsstatement and proof · cited by 4
- ConvexOn.locallyLipschitzOnproof · cited by 3
- AffineBasis.affineCombination_coord_eq_selfstatement and proof · cited by 3