Theorems · Theorem · linear algebra
add_dotProduct
∀ {m : Type u_2} {α : Type v} [inst : Fintype m] [inst_1 : NonUnitalNonAssocSemiring α] (u v w : m → α),
(u + v) ⬝ᵥ w = u ⬝ᵥ w + v ⬝ᵥ w- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- add_mulproof · cited by 363
- dotProductstatement · cited by 194
- Finset.sum_add_distribproof · cited by 131
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.add_mulproof · cited by 9
- Matrix.add_mulVecproof · cited by 7
- sub_dotProductproof · cited by 3
- Matrix.add_vecMulproof · cited by 2
- FirstOrder.Language.presburger.term_realize_eq_add_dotProductproof · cited by 1
- Matrix.schur_complement_eq₁₁proof · cited by 1
- Matrix.schur_complement_eq₂₂proof · cited by 0