Theorems · Theorem · linear algebra
crossProduct_ne_zero_iff_linearIndependent
∀ {F : Type u_2} [inst : Field F] {v w : Fin 3 → F}, (crossProduct v) w ≠ 0 ↔ LinearIndependent F ![v, w]- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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 and proof · cited by 18,349
- LinearMapstatement and proof · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- mul_commproof · cited by 2,262
- map_zeroproof · cited by 1,614
- Matrix.vecConsstatement and proof · cited by 852
- Matrix.vecEmptystatement and proof · cited by 832
- smul_zeroproof · cited by 665
- map_smulproof · cited by 566
- LinearIndependentstatement and proof · cited by 560
- neg_smulproof · cited by 306
Cited by1
Results whose statement or proof uses this declaration.
- Projectivization.mk_eq_mk_iff_crossProduct_eq_zeroproof · cited by 5