Theorems · Definition · number theory
QuadraticMap.polarBilin
{R : Type u_3} →
{M : Type u_4} →
{N : Type u_5} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] →
[inst_2 : AddCommGroup N] →
[inst_3 : Module R M] → [inst_4 : Module R N] → QuadraticMap R M N → LinearMap.BilinMap R M NQuadraticMap.polar as a bilinear map
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, 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.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- QuadraticMapstatement and proof · cited by 262
- LinearMap.BilinMapstatement · cited by 85
- QuadraticMap.polarproof · cited by 50
- QuadraticMap.polar_smul_leftproof · cited by 5
- QuadraticMap.polar_smul_rightproof · cited by 5
- LinearMap.mk₂proof · cited by 5
- QuadraticMap.polar_add_leftproof · cited by 2
- QuadraticMap.polar_add_rightproof · cited by 1
Cited by29
Results whose statement or proof uses this declaration.
- QuadraticMap.associatedHomproof · cited by 29
- QuadraticMap.radicalproof · cited by 13
- QuadraticMap.polarBilin_apply_applystatement and proof · cited by 11
- QuadraticMap.radical_eq_ker_polarBilinstatement · cited by 3
- QuadraticMap.two_nsmul_associatedstatement · cited by 2
- baseChange_extproof · cited by 2
- QuadraticMap.map_sumproof · cited by 2
- QuadraticMap.polarBilin_prodstatement · cited by 1
- QuadraticMap.Ring.polarBilin_pistatement and proof · cited by 1
- QuadraticForm.polarBilin_tmulstatement and proof · cited by 1
- QuadraticMap.isOrtho_polarBilinstatement and proof · cited by 1
- QuadraticMap.map_sum'proof · cited by 1