Theorems · Theorem · linear algebra
smul_dotProduct
∀ {m : Type u_2} {R : Type u_7} {α : Type v} [inst : Fintype m] [inst_1 : Mul α] [inst_2 : AddCommMonoid α]
[inst_3 : DistribSMul R α] [IsScalarTower R α α] (x : R) (v w : m → α), x • v ⬝ᵥ w = x • (v ⬝ᵥ w)- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 5 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- IsScalarTowerstatement and proof · cited by 3,896
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- dotProductstatement · cited by 194
- DistribSMulstatement and proof · cited by 117
- Finset.smul_sumproof · cited by 88
- smul_mul_assocproof · cited by 77
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.smul_mulproof · cited by 11
- Matrix.smul_mulVecproof · cited by 5
- Matrix.smul_vecMulproof · cited by 2
- Matrix.IsHadamard.card_eq_mul_star_of_const_col_sumproof · cited by 1
- Matrix.IsHermitian.eigenvalues_eqproof · cited by 1