Theorems · Definition · number theory
QuadraticMap.polar
{M : Type u_4} → {N : Type u_5} → [AddCommGroup M] → [AddCommGroup N] → (M → N) → M → M → NUp to a factor 2, Q.polar is the associated bilinear map for a quadratic map Q.
Source of this name: https://en.wikipedia.org/wiki/Quadratic_form#Generalization
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddCommGroupAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
Cited by54
Results whose statement or proof uses this declaration.
- QuadraticMap.polarBilinproof · cited by 25
- QuadraticMap.polarBilin_apply_applystatement · cited by 11
- QuadraticMap.polarSym2proof · cited by 11
- QuadraticMap.toBilinproof · cited by 6
- QuadraticMap.polar_smul_leftstatement · cited by 5
- QuadraticMap.polar_smul_rightstatement and proof · cited by 5
- QuadraticMap.polar_commstatement and proof · cited by 3
- QuadraticMap.polar_selfstatement · cited by 3
- QuadraticMap.toBilin_applystatement and proof · cited by 3
- lipschitzGroup.conjAct_smul_ι_mem_range_ιproof · cited by 3
- QuadraticMap.map_addstatement · cited by 3
- CliffordAlgebra.ι_mul_ι_add_swapstatement · cited by 3