Theorems · Theorem · number theory
QuadraticMap.associated_linMulLin
∀ {R : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : Invertible 2] (f g : M →ₗ[R] R),
QuadraticMap.associated (QuadraticMap.linMulLin f g) =
⅟2 • ((LinearMap.mul R R).compl₁₂ f g + (LinearMap.mul R R).compl₁₂ g f)- Cited by
- 1 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- map_addproof · cited by 964
- pow_oneproof · cited by 894
- LinearMap.extproof · cited by 844
- Invertiblestatement and proof · cited by 549
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticMap.associated_sqproof · cited by 3