Theorems · Theorem · linear algebra
LinearEquiv.symm_flip
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : AddCommGroup N] [inst_4 : Module R N] [inst_5 : Module.IsReflexive R M] (e : N ≃ₗ[R] Module.Dual R M),
e.flip.symm = e.symm.dualMap ≪≫ₗ (Module.evalEquiv R M).symm- Cited by
- 0 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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 and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmstatement · cited by 1,461
- Module.Dualstatement and proof · cited by 583
- LinearEquiv.transstatement · cited by 298
- Module.IsReflexivestatement and proof · cited by 58
- LinearEquiv.dualMapstatement · cited by 20
- Module.evalEquivstatement · cited by 14
- LinearEquiv.flipstatement · cited by 10
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