Theorems · Theorem · linear algebra
Matrix.vecMul_eq_sum
∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype m] (v : m → α)
(M : Matrix m n α), Matrix.vecMul v M = ∑ i, v i • M i- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.sumstatement · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.vecMulstatement · cited by 148
- Finset.sum_fnproof · cited by 21
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.vecMul_injective_iffproof · cited by 4
- Matrix.dot_mulVec_eq_sum_sumproof · cited by 1
- RootPairing.Base.injective_pairingInproof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1
- Matrix.vecMul_permMatrixproof · cited by 0