diff --git a/docs/src/lib/conversion.md b/docs/src/lib/conversion.md
index 4267bb518c..728f0f268b 100644
--- a/docs/src/lib/conversion.md
+++ b/docs/src/lib/conversion.md
@@ -43,5 +43,9 @@ convert(::Type{Zonotope}, ::CartesianProduct{N, Zonotope{N}, Zonotope{N}}) where
 convert(::Type{Hyperrectangle}, ::CartesianProduct{N, HN1, HN2}) where {N<:Real, HN1<:AbstractHyperrectangle{N}, HN2<:AbstractHyperrectangle{N}}
 convert(::Type{Zonotope}, ::CartesianProduct{N, HN1, HN2}) where {N<:Real, HN1<:AbstractHyperrectangle{N}, HN2<:AbstractHyperrectangle{N}}
 convert(::Type{Zonotope}, ::CartesianProductArray{N, HN}) where {N<:Real, HN<:AbstractHyperrectangle{N}}
-convert(::Type{Zonotope}, ::LinearMap{N, SN, NM, MAT}) where {N, SN<:AbstractHyperrectangle{N}, NM, MAT<:AbstractMatrix{N}}
+convert(::Type{Zonotope}, ::LinearMap{N, SN}) where {N, SN<:AbstractHyperrectangle{N}}
+convert(::Type{Zonotope}, ::LinearMap{N, CartesianProduct{N, HN1, HN2}}) where {N, HN1<:AbstractHyperrectangle{N}, HN2<:AbstractHyperrectangle{N}}
+convert(::Type{Zonotope}, ::LinearMap{N, CartesianProductArray{N, HN}}) where {N, HN<:AbstractHyperrectangle{N}}
 ```
+
+
diff --git a/src/convert.jl b/src/convert.jl
index 642b059c7a..f0fef4f77f 100644
--- a/src/convert.jl
+++ b/src/convert.jl
@@ -305,8 +305,8 @@ end
 
 """
     convert(::Type{Zonotope},
-            S::LinearMap{N, SN, NM, MAT}
-            ) where {N, SN<:AbstractHyperrectangle{N}, NM, MAT<:AbstractMatrix{N}}
+            S::LinearMap{N, SN}
+            ) where {N, SN<:AbstractHyperrectangle{N}}
 
 Converts the lazy linear map of a hyperrectangular set to a zonotope.
 
@@ -324,11 +324,64 @@ A zonotope.
 This method first converts the hyperrectangular set to a zonotope, and then
 applies the (concrete) linear map to the zonotope.
 """
+function convert(::Type{Zonotope}, S::LinearMap{N, SN}
+                ) where {N, SN<:AbstractHyperrectangle{N}}
+    return linear_map(S.M, convert(Zonotope, S.X))
+end
+
+"""
+    convert(::Type{Zonotope}, S::LinearMap{N, CartesianProduct{N, HN1, HN2}}
+           ) where {N, HN1<:AbstractHyperrectangle{N},
+                    HN2<:AbstractHyperrectangle{N}}
+
+Converts the lazy linear map of the cartesian product of two hyperrectangular
+sets to a zonotope.
+
+### Input
+
+- `Zonotope` -- type, used for dispatch
+- `S`        -- linear map of the cartesian product of hyperrectangular sets
+
+### Output
+
+A zonotope.
+
+### Algorithm
+
+This method first converts the cartesian product to a zonotope, and then
+applies the (concrete) linear map to the zonotope.
+"""
 function convert(::Type{Zonotope},
-                 S::LinearMap{N, SN, NM, MAT}
-                 ) where {N, SN<:AbstractHyperrectangle{N}, NM, MAT<:AbstractMatrix{N}}
-    Xz = convert(Zonotope, S.X)
-    return linear_map(S.M, Xz)
+                 S::LinearMap{N, CartesianProduct{N, HN1, HN2}}
+                ) where {N, HN1<:AbstractHyperrectangle{N},
+                         HN2<:AbstractHyperrectangle{N}}
+    return linear_map(S.M, convert(Zonotope, S.X))
+end
+
+"""
+    convert(::Type{Zonotope},S::LinearMap{N, CartesianProductArray{N, HN}}
+           ) where {N, HN<:AbstractHyperrectangle{N}}
+
+Converts the lazy linear map of the cartesian product of a finite number of
+hyperrectangular sets to a zonotope.
+
+### Input
+
+- `Zonotope` -- type, used for dispatch
+- `S`        -- linear map of a `CartesianProductArray` of hyperrectangular sets
+
+### Output
+
+A zonotope.
+
+### Algorithm
+
+This method first converts the cartesian product array to a zonotope, and then
+applies the (concrete) linear map to the zonotope.
+"""
+function convert(::Type{Zonotope}, S::LinearMap{N, CartesianProductArray{N, HN}}
+                ) where {N, HN<:AbstractHyperrectangle{N}}
+    return linear_map(S.M, convert(Zonotope, S.X))
 end
 
 """
diff --git a/test/unit_Zonotope.jl b/test/unit_Zonotope.jl
index 53c07bcbbf..94a1b852a6 100644
--- a/test/unit_Zonotope.jl
+++ b/test/unit_Zonotope.jl
@@ -129,6 +129,17 @@ for N in [Float64, Rational{Int}, Float32]
     Z = convert(Zonotope, M * B)
     @test Z isa Zonotope && Z.center == N[0] && Z.generators == hcat(N[1])
 
+    # conversion of the lazy linear map of the cartesian product of hyperrectangular
+    # sets to a zonotope
+    B = BallInf(N[0], N(1))
+    M = N[1 0; 0 -1]
+    Z = convert(Zonotope, M * (B × B))
+    @test Z isa Zonotope && Z.center == N[0, 0] && Z.generators == M
+
+    # same for CPA
+    Z2 = convert(Zonotope, M * CartesianProductArray([B, B]))
+    @test Z2 == Z
+
     # list of constraints
     Z = Zonotope(zeros(N, 3), Matrix(N(1)*I, 3, 3))
     B = BallInf(zeros(N, 3), N(1)) # equivalent to Z