diff --git a/docs/src/lib/representations.md b/docs/src/lib/representations.md
index 070ce6c2b9..4f8100b7d3 100644
--- a/docs/src/lib/representations.md
+++ b/docs/src/lib/representations.md
@@ -175,6 +175,7 @@ constrained_dimensions(::HalfSpace{N}) where {N<:Real}
 halfspace_left(::AbstractVector{N}, ::AbstractVector{N}) where {N<:Real}
 halfspace_right(::AbstractVector{N}, ::AbstractVector{N}) where {N<:Real}
 tosimplehrep(::AbstractVector{HalfSpace{N}}) where {N<:Real}
+linear_map(::AbstractMatrix{N}, ::HalfSpace{N}) where {N}
 ```
 Inherited from [`LazySet`](@ref):
 * [`norm`](@ref norm(::LazySet, ::Real))
diff --git a/src/HalfSpace.jl b/src/HalfSpace.jl
index 0d4d889557..5c5553be76 100644
--- a/src/HalfSpace.jl
+++ b/src/HalfSpace.jl
@@ -6,7 +6,8 @@ import Base: rand,
 export HalfSpace, LinearConstraint,
        an_element,
        constrained_dimensions,
-       halfspace_left, halfspace_right
+       halfspace_left, halfspace_right,
+       linear_map
 
 """
     HalfSpace{N<:Real} <: LazySet{N}
@@ -356,3 +357,21 @@ function halfspace_right(p::AbstractVector{N},
                          q::AbstractVector{N})::HalfSpace{N} where {N<:Real}
     return halfspace_left(q, p)
 end
+
+"""
+    linear_map(M::AbstractMatrix{N}, hs::HalfSpace{N}) where {N}
+
+Return the concrete linear map of a half-space.
+
+### Input
+
+- `M`  -- matrix
+- `hs` -- half-space
+
+### Output
+
+The half-space obtained by applying the given linear map to the half-space.
+"""
+function linear_map(M::AbstractMatrix{N}, hs::HalfSpace{N}) where {N}
+    return linear_map(M, HPolyhedron([hs]))
+end
diff --git a/test/unit_HalfSpace.jl b/test/unit_HalfSpace.jl
index 7f3eeb0abe..8ea33729b7 100644
--- a/test/unit_HalfSpace.jl
+++ b/test/unit_HalfSpace.jl
@@ -81,4 +81,10 @@ for N in [Float64, Rational{Int}, Float32]
     hs4 = HalfSpace(N[-1, 0], N(0)) # x >= 0
     empty_intersection, v = is_intersection_empty(hs1, hs4, true)
     @test !is_intersection_empty(hs1, hs4) && !empty_intersection && v ∈ hs1 && v ∈ hs4
+
+    # test linear map of a half-space
+    H = HalfSpace(N[1.0, -1.0], N(0.0)) # x <= y
+    M = Matrix(-N(1.0)*I, 2, 2)
+    MH = linear_map(M, H)
+    @test constraints_list(MH)[1] == HalfSpace(N[-1.0, 1.0], N(0.0)) # x >= y
 end