Theorems · Definition · ring theory
Quaternion
(R : Type u_1) → [Zero R] → [One R] → [Neg R] → Type u_1
Space of quaternions over a type, denoted as ℍ[R].
Implemented as a structure with four fields: re, im_i, im_j, and im_k.
- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 206 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 13 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- QuaternionAlgebraproof · cited by 174
Cited by216
Results whose statement or proof uses this declaration.
- Quaternion.coestatement · cited by 68
- Quaternion.normSqstatement and proof · cited by 31
- Quaternion.imstatement and proof · cited by 27
- Quaternion.dualNumberEquivstatement and proof · cited by 16
- Quaternion.coeComplexstatement · cited by 11
- Quaternion.extstatement and proof · cited by 6
- Quaternion.linearIsometryEquivTuplestatement and proof · cited by 6
- Quaternion.coe_mulstatement · cited by 5
- Quaternion.equivProdstatement · cited by 5
- Quaternion.normSq_coestatement and proof · cited by 5
- Quaternion.normSq_def'statement and proof · cited by 5
- Quaternion.re_starstatement and proof · cited by 4
Showing the 200 most cited of 216.