Theorems · Theorem · linear algebra
LinearMap.IsPerfPair.flip
∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] [inst_2 : CommRing R]
[inst_3 : Module R M] [inst_4 : Module R N] {p : M →ₗ[R] N →ₗ[R] R}, p.IsPerfPair → p.flip.IsPerfPairGiven a perfect pairing between M and N, we may interchange the roles of M and N.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LinearMapstatement and proof · cited by 10,215
- LinearMap.flipstatement · cited by 193
- LinearMap.IsPerfPairstatement and proof · cited by 34
- LinearMap.IsPerfPair.bijective_leftproof · cited by 1
- LinearMap.IsPerfPair.bijective_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsPerfPair.of_injective'proof · cited by 0