Theorems · Definition · linear algebra
crossProduct
{R : Type u_1} → [inst : CommRing R] → (Fin 3 → R) →ₗ[R] (Fin 3 → R) →ₗ[R] Fin 3 → RThe cross product of two vectors in $R^3$ for $R$ a commutative ring.
- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- LinearMap.mk₂proof · cited by 5
Cited by28
Results whose statement or proof uses this declaration.
- Projectivization.crossproof · cited by 10
- Projectivization.mk_eq_mk_iff_crossProduct_eq_zerostatement and proof · cited by 5
- cross_anticommstatement · cited by 5
- dot_self_crossstatement · cited by 2
- Projectivization.cross_mkstatement and proof · cited by 2
- cross_applystatement · cited by 2
- cross_selfstatement · cited by 2
- Projectivization.cross_mk_of_nestatement and proof · cited by 2
- Projectivization.cross_orthogonal_leftproof · cited by 2
- Projectivization.cross_commproof · cited by 1
- InnerProductGeometry.norm_ofLp_crossProductstatement and proof · cited by 1
- Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zerostatement and proof · cited by 1