Theorems · Definition · linear algebra
dotProduct
{m : Type u_2} → {α : Type v} → [Fintype m] → [Mul α] → [AddCommMonoid α] → (m → α) → (m → α) → αdotProduct v w is the sum of the entrywise products v i * w i.
See also dotProductEquiv.
- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 194 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 96 definitions · uses propext, Quot.sound
- Assumes
- FintypeMulAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Finset.univproof · cited by 3,473
Cited by202
Results whose statement or proof uses this declaration.
- Matrix.mulVecproof · cited by 267
- Matrix.vecMulproof · cited by 148
- Matrix.SeparatingRightproof · cited by 35
- Matrix.SeparatingLeftproof · cited by 33
- Matrix.dotProduct_mulVecstatement · cited by 19
- dotProduct_commstatement · cited by 13
- dotProduct_zerostatement · cited by 11
- Projectivization.orthogonalproof · cited by 10
- Matrix.toLinearMap₂'_apply'statement and proof · cited by 10
- single_dotProductstatement and proof · cited by 10
- zero_dotProductstatement · cited by 9
- Matrix.PosDef.dotProduct_mulVec_posstatement · cited by 7
Showing the 200 most cited of 202.