Theorems · Theorem · linear algebra
dotProduct_neg
∀ {m : Type u_2} {α : Type v} [inst : Fintype m] [inst_1 : NonUnitalNonAssocRing α] (v w : m → α), v ⬝ᵥ -w = -(v ⬝ᵥ w)- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeNonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- mul_negproof · cited by 590
- NonUnitalNonAssocRingstatement and proof · cited by 354
- dotProductstatement · cited by 194
- Finset.sum_neg_distribproof · cited by 65
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.mul_negproof · cited by 5
- dotProduct_subproof · cited by 2
- Matrix.vecMul_negproof · cited by 2
- Matrix.mulVec_negproof · cited by 1
- neg_dotProduct_negproof · cited by 0
- dot_cross_selfproof · cited by 0