Theorems · Definition · convex and discrete geometry

ConvexCone.map

{R : Type u_2} →
  {M : Type u_4} →
    {N : Type u_5} →
      [inst : Semiring R] →
        [inst_1 : PartialOrder R] →
          [inst_2 : AddCommMonoid M] →
            [inst_3 : AddCommMonoid N] →
              [inst_4 : Module R M] → [inst_5 : Module R N] → (M →ₗ[R] N) → ConvexCone R M → ConvexCone R N

The image of a convex cone under an R-linear map is a convex cone.

Defined in

Mathlib.Geometry.Convex.Cone.Basic

Cited by

5 results in Mathlib

Foundations

Depth 24 from the axioms · uses no axioms

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidModuleModule