Theorems · Theorem · nonassociative algebras
RootPairing.flip_toLinearMap
∀ {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),
P.flip.toLinearMap = P.flip- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- RootPairingstatement and proof · cited by 710
- LinearMap.flipstatement · cited by 193
- RootPairing.toLinearMapstatement and proof · cited by 108
- RootPairing.flipstatement and proof · cited by 79
- SMulCommClass.symmstatement · cited by 67
Cited by4
Results whose statement or proof uses this declaration.
- RootPairing.polarization_apply_eq_zero_iffproof · cited by 2
- RootPairing.rootSpan_dualAnnihilator_map_eqproof · cited by 2
- RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root'proof · cited by 2
- RootPairing.polarizationEquiv_toLinearMapproof · cited by 1