Theorems · Definition · linear algebra
Module.Basis.orientation
{R : Type u_1} →
[inst : CommRing R] →
[inst_1 : PartialOrder R] →
[inst_2 : IsStrictOrderedRing R] →
{M : Type u_2} →
[inst_3 : AddCommGroup M] →
[inst_4 : Module R M] →
{ι : Type u_4} → [Fintype ι] → [DecidableEq ι] → Module.Basis ι R M → Orientation R M ιThe orientation given by a basis.
- Defined in
- Mathlib.LinearAlgebra.Orientation
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 97 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.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Module.Basisstatement and proof · cited by 1,477
- Orientationstatement · cited by 360
- Module.Basis.detproof · cited by 73
- rayOfNeZeroproof · cited by 22
Cited by30
Results whose statement or proof uses this declaration.
- Complex.orientationproof · cited by 10
- Module.Basis.adjustToOrientationproof · cited by 7
- Orientation.volumeForm_neg_orientationproof · cited by 6
- OrthonormalBasis.volume_parallelepipedproof · cited by 4
- Orientation.finOrthonormalBasis_orientationstatement · cited by 4
- Orientation.volumeForm_robuststatement and proof · cited by 4
- Module.Basis.orientation_mapstatement · cited by 3
- Module.Basis.adjustToOrientation_apply_eq_or_eq_negproof · cited by 2
- Module.Basis.orientation_adjustToOrientationstatement and proof · cited by 2
- Module.Basis.orientation_eq_iff_det_posstatement · cited by 2
- Module.Basis.orientation_eq_or_eq_negstatement · cited by 2
- Module.Basis.orientation_isEmptystatement · cited by 2