Theorems · Definition · linear algebra
Module.Ray
(R : Type u_1) →
[inst : CommSemiring R] →
[inst_1 : PartialOrder R] →
[IsStrictOrderedRing R] → (M : Type u_2) → [inst_3 : AddCommMonoid M] → [Module R M] → Type u_2A ray (equivalence class of nonzero vectors with common positive multiples) in a module.
- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 29 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
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
Cited by35
Results whose statement or proof uses this declaration.
- Orientationproof · cited by 360
- rayOfNeZerostatement · cited by 22
- Module.Ray.indstatement and proof · cited by 10
- ray_eq_iffstatement · cited by 8
- Module.Ray.mapstatement · cited by 7
- rayOfNeZero.congr_simpstatement · cited by 4
- units_inv_smulstatement and proof · cited by 4
- Orientation.map_eq_iff_det_posproof · cited by 3
- smul_rayOfNeZerostatement · cited by 3
- units_smul_eq_self_iffstatement and proof · cited by 3
- Module.Basis.map_orientation_eq_det_inv_smulproof · cited by 3
- Module.Ray.ne_neg_selfstatement and proof · cited by 3