Theorems · Theorem · linear algebra
cross_apply
∀ {R : Type u_1} [inst : CommRing R] (a b : Fin 3 → R),
(crossProduct a) b = ![a 1 * b 2 - a 2 * b 1, a 2 * b 0 - a 0 * b 2, a 0 * b 1 - a 1 * b 0]- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Matrix.vecConsstatement · cited by 852
- Matrix.vecEmptystatement · cited by 832
- crossProductstatement · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- dot_self_crossproof · cited by 2
- triple_product_eq_detproof · cited by 0