Theorems · Theorem · linear algebra
triple_product_eq_det
∀ {R : Type u_1} [inst : CommRing R] (u v w : Fin 3 → R), u ⬝ᵥ (crossProduct v) w = Matrix.det ![u, v, w]The triple product of u, v, and w is equal to the determinant of the matrix
with those vectors as its rows.
- Defined in
- Mathlib.LinearAlgebra.CrossProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 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.
Cites12
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
- Matrix.vecConsstatement and proof · cited by 852
- Matrix.vecEmptystatement and proof · cited by 832
- Matrix.detstatement and proof · cited by 665
- dotProductstatement · cited by 194
- crossProductstatement and proof · cited by 27
- Matrix.vec3_dotProductproof · cited by 6
- Matrix.det_fin_threeproof · cited by 3
- cross_applyproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.