Theorems · Theorem · linear algebra
CliffordAlgebraQuaternion.toQuaternion_star
∀ {R : Type u_1} [inst : CommRing R] {c₁ c₂ : R} (c : CliffordAlgebra (CliffordAlgebraQuaternion.Q c₁ c₂)),
CliffordAlgebraQuaternion.toQuaternion (star c) = star (CliffordAlgebraQuaternion.toQuaternion c)The "clifford conjugate" maps to the quaternion conjugate.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CommRingstatement and proof · cited by 17,173
- AlgHomstatement · cited by 3,236
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- MulZeroClass.zero_mulproof · cited by 1,625
- map_mulproof · cited by 1,137
- Star.starstatement and proof · cited by 1,082
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- neg_zeroproof · cited by 542
- map_negproof · cited by 378
- CliffordAlgebrastatement and proof · cited by 309
- QuaternionAlgebrastatement · cited by 174
Cited by1
Results whose statement or proof uses this declaration.
- CliffordAlgebraQuaternion.ofQuaternion_starproof · cited by 0