diff --git a/src/concrete_intersection.jl b/src/concrete_intersection.jl
index e5402ac99d..210c0e518b 100644
--- a/src/concrete_intersection.jl
+++ b/src/concrete_intersection.jl
@@ -806,8 +806,8 @@ function intersection(X::CartesianProductArray{N},
                       oa=Hyperrectangle) where {N}
 
     low_set, vars, block_structure = initialize_vars(X, blocks)
-
-    low_intersection = intersection(low_set, Approximations.project(Y, vars, LinearMap))
+    
+    low_intersection = intersection(low_set, Approximations.project(Y, vars))
 
     if isempty(low_intersection)
         return EmptySet()
diff --git a/src/helper_functions.jl b/src/helper_functions.jl
index 0ef8ec7761..eacd4be7a1 100644
--- a/src/helper_functions.jl
+++ b/src/helper_functions.jl
@@ -4,8 +4,8 @@ export _At_mul_B
 const DEFAULT_COND_TOL = 1e6
 
 # matrix-matrix multiplication and division
-@inline _At_mul_B(A, B) = transpose(Matrix(A)) * B
-@inline _At_ldiv_B(A, B) = transpose(Matrix(A)) \ B
+@inline _At_mul_B(A, B) = transpose(A) * B
+@inline _At_ldiv_B(A, B) = transpose(A) \ B
 
 """
     dot_zero(x::AbstractVector{N}, y::AbstractVector{N}) where{N<:Real}
@@ -159,13 +159,13 @@ We check whether the matrix is square and whether the
 `cond(M)` is below some prescribed tolerance.
 """
 function isinvertible(M::Matrix; cond_tol::Number=DEFAULT_COND_TOL)
-    return cond(M) < cond_tol
+    return issquare(M) && cond(M) < cond_tol
 end
 
 # cond is not available for sparse matrices; see JuliaLang#6485 and related issues
 function isinvertible(M::AbstractSparseMatrix;
                       cond_tol::Number=DEFAULT_COND_TOL)
-     return isinvertible(Matrix(M), cond_tol=cond_tol)
+     return issquare(M) && isinvertible(Matrix(M), cond_tol=cond_tol)
 end
 
 function isinvertible(M::Diagonal; cond_tol=nothing)
@@ -542,9 +542,9 @@ julia> subtypes(AbstractPolytope, true)
 function subtypes(interface, concrete::Bool)
 
     subtypes_to_test = subtypes(interface)
-    
+
     # do not seek the concrete subtypes further
-    if !concrete 
+    if !concrete
         return sort(subtypes_to_test, by=string)
     end
 
diff --git a/test/unit_CartesianProduct.jl b/test/unit_CartesianProduct.jl
index e14b6a026c..988b2f2475 100644
--- a/test/unit_CartesianProduct.jl
+++ b/test/unit_CartesianProduct.jl
@@ -279,7 +279,6 @@ end
 
 for N in [Float64, Float32]
     #intersection and is_intersection_empty
-    intersection and is_intersection_empty
     i1 = Interval(N[0, 1])
     i2 = Interval(N[2, 3])
     h1 = Hyperrectangle(low=N[3, 4], high=N[5, 7])