Theorems · Theorem · linear algebra
dot_self_cross
∀ {R : Type u_1} [inst : CommRing R] (v w : Fin 3 → R), v ⬝ᵥ (crossProduct v) w = 0The cross product of two vectors is perpendicular to the first vector.
- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Nat.cast_zeroproof · cited by 1,870
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- dotProductstatement and proof · cited by 194
- crossProductstatement · cited by 27
- Matrix.vec3_dotProductproof · cited by 6
- cross_applyproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Projectivization.cross_orthogonal_leftproof · cited by 2
- dot_cross_selfproof · cited by 0