Theorems · Theorem · linear algebra
Matrix.dotProduct_mulVec
∀ {m : Type u_2} {n : Type u_3} {R : Type u_7} [inst : Fintype n] [inst_1 : Fintype m] [inst_2 : NonUnitalSemiring R]
(v : m → R) (A : Matrix m n R) (w : n → R), v ⬝ᵥ A.mulVec w = Matrix.vecMul v A ⬝ᵥ wAssociate the dot product of mulVec to the left.
- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- mul_assocproof · cited by 1,667
- NonUnitalSemiringstatement and proof · cited by 339
- Matrix.mulVecstatement · cited by 267
- Finset.mul_sumproof · cited by 196
- dotProductstatement · cited by 194
- Matrix.vecMulstatement · cited by 148
- Finset.sum_mulproof · cited by 112
- Finset.sum_commproof · cited by 66
Cited by19
Results whose statement or proof uses this declaration.
- Matrix.dotProduct_transpose_mulVecproof · cited by 3
- Matrix.posSemidef_conjTranspose_mul_selfproof · cited by 3
- Matrix.PosSemidef.conjTranspose_mul_mul_sameproof · cited by 3
- Matrix.PosSemidef.posDef_iff_isUnitproof · cited by 3
- Matrix.PosDef.conjTranspose_mul_mul_sameproof · cited by 3
- Matrix.separatingLeft_iff_forall_vecMul_eq_zeroproof · cited by 2
- Matrix.dot_mulVec_eq_sum_sumproof · cited by 1
- LDL.diag_eq_lowerInv_conjproof · cited by 1
- Matrix.PosSemidef.dotProduct_mulVec_zero_iffproof · cited by 1
- Matrix.ker_mulVecLin_transpose_mul_selfproof · cited by 1
- Matrix.IsHadamard.card_eq_mul_star_of_const_col_sumproof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1