Theorems · Theorem · convex and discrete geometry

PointedCone.dual_eq_dual_id_image

∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {N : Type u_3} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
  {p : M →ₗ[R] N →ₗ[R] R} (s : Set M), PointedCone.dual p s = PointedCone.dual LinearMap.id (⇑p '' s)

Duality with respect to a general bilinear map can be expressed as duality using the identity pairing.

Defined in

Mathlib.Geometry.Convex.Cone.Dual

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsOrderedRingAddCommMonoidModuleAddCommMonoidModule