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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 N

QuadraticMap.polar as a bilinear map

Defined in
Mathlib.LinearAlgebra.QuadraticForm.Basic
Cited by
25 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Quot.sound
Assumes
CommRingAddCommGroupAddCommGroupModuleModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

QuadraticMap.associatedHom · cited by 29QuadraticMap.associatedHomQuadraticMap.radical · cited by 13QuadraticMap.radicalQuadraticMap.polarBilin_apply_apply · cited by 11QuadraticMap.polarBilin_a…QuadraticMap.radical_eq_ker_polarBilin · cited by 3QuadraticMap.radical_eq_k…QuadraticMap.two_nsmul_associated · cited by 2QuadraticMap.two_nsmul_as…baseChange_ext · cited by 2baseChange_extQuadraticMap.map_sum · cited by 2QuadraticMap.map_sumQuadraticMap.polarBilin_prod · cited by 1QuadraticMap.polarBilin_p…QuadraticMap.Ring.polarBilin_pi · cited by 1Ring.polarBilin_piQuadraticForm.polarBilin_tmul · cited by 1QuadraticForm.polarBilin_…QuadraticMap.isOrtho_polarBilin · cited by 1QuadraticMap.isOrtho_pola…QuadraticMap.map_sum' · cited by 1QuadraticMap.map_sum'QuadraticMap.polarBilin_comp · cited by 0QuadraticMap.polarBilin_c…QuadraticMap.polarBilin_injective · cited by 0QuadraticMap.polarBilin_i…QuadraticMap.Ring.associated_pi · cited by 0Ring.associated_piDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupQuadraticMap · cited by 262QuadraticMapLinearMap.BilinMap · cited by 85LinearMap.BilinMapQuadraticMap.polar · cited by 50QuadraticMap.polarQuadraticMap.polar_smul_left · cited by 5QuadraticMap.polar_smul_l…QuadraticMap.polar_smul_right · cited by 5QuadraticMap.polar_smul_r…LinearMap.mk₂ · cited by 5LinearMap.mk₂QuadraticMap.polar_add_left · cited by 2QuadraticMap.polar_add_le…QuadraticMap.polar_add_right · cited by 1QuadraticMap.polar_add_ri…QuadraticMap.polarBilinCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by29

Results whose statement or proof uses this declaration.