Theorems · Theorem · nonassociative algebras

RootPairing.polarization_apply_eq_zero_iff

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N) [inst_5 : Fintype ι]
  (m : M), P.Polarization m = 0 ↔ P.RootForm m = 0

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear
Cited by: 2 results in Mathlib
Foundations: Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Fintype

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Cites19

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
Fintypestatement and proof · cited by 7,736
LinearMap.compproof · cited by 1,642
map_zeroproof · cited by 1,614
RootPairingstatement and proof · cited by 710
LinearMap.BilinFormstatement · cited by 501
LinearMap.comp.congr_simpproof · cited by 209

Cited by2

Results whose statement or proof uses this declaration.

RootPairing.ker_polarization_eq_ker_rootFormproof · cited by 2
RootPairing.coPolarization_apply_eq_zero_iffproof · cited by 0