Theorems · Theorem · linear algebra
dot_cross_self
∀ {R : Type u_1} [inst : CommRing R] (v w : Fin 3 → R), w ⬝ᵥ (crossProduct v) w = 0The cross product of two vectors is perpendicular to the second vector.
- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- neg_zeroproof · cited by 542
- dotProductstatement and proof · cited by 194
- crossProductstatement and proof · cited by 27
- dotProduct_negproof · cited by 6
- cross_anticommproof · cited by 5
- dot_self_crossproof · cited by 2
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