Theorems · Theorem · number theory
QuadraticMap.weightedSumSquares_apply
∀ {S : Type u_1} {R : Type u_3} [inst : CommSemiring R] {ι : Type u_8} [inst_1 : Fintype ι] [inst_2 : Monoid S]
[inst_3 : DistribMulAction S R] [inst_4 : SMulCommClass S R R] (w : ι → S) (v : ι → R),
(QuadraticMap.weightedSumSquares R w) v = ∑ i, w i • (v i * v i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 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.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Monoidstatement and proof · cited by 3,887
- Finset.univstatement and proof · cited by 3,473
- SMulCommClassstatement and proof · cited by 1,927
- DistribMulActionstatement and proof · cited by 584
- QuadraticMapstatement · cited by 262
- sum_applyproof · cited by 83
- QuadraticMap.weightedSumSquaresstatement · cited by 18
- QuadraticMap.projproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- QuadraticForm.sigNeg_weightedSumSquaresproof · cited by 1
- QuadraticForm.radical_weightedSumSquaresproof · cited by 1
- QuadraticMap.basisRepr_eq_of_iIsOrthoproof · cited by 0