diff --git a/src/HPolyhedron.jl b/src/HPolyhedron.jl
index 0b85e43168..846e322321 100644
--- a/src/HPolyhedron.jl
+++ b/src/HPolyhedron.jl
@@ -502,14 +502,17 @@ function remove_redundant_constraints!(P::PT;
 end
 
 """
-    linear_map(M::AbstractMatrix{N}, P::PT) where {N<:Real, PT<:HPoly{N}}
+    linear_map(M::AbstractMatrix{N}, P::PT; [cond_tol=DEFAULT_COND_TOL]::Number)
+        where {N<:Real, PT<:HPoly{N}}
 
 Concrete linear map of a polyhedron in constraint representation.
 
 ### Input
 
-- `M` -- matrix
-- `P` -- polyhedron in constraint representation
+- `M`        -- matrix
+- `P`        -- polyhedron in constraint representation
+- `cond_tol` -- (optional) tolerance of matrix condition (used to check whether
+                the matrix is invertible)
 
 ### Output
 
@@ -521,8 +524,11 @@ If the matrix ``M`` is invertible (which we check with a sufficient condition),
 then ``y = M x`` implies ``x = \\text{inv}(M) y`` and we transform the
 constraint system ``A x ≤ b`` to ``A \\text{inv}(M) y ≤ b``.
 """
-function linear_map(M::AbstractMatrix{N}, P::PT) where {N<:Real, PT<:HPoly{N}}
-    if !isinvertible(M)
+function linear_map(M::AbstractMatrix{N},
+                    P::PT;
+                    cond_tol::Number=DEFAULT_COND_TOL
+                   ) where {N<:Real, PT<:HPoly{N}}
+    if !isinvertible(M; cond_tol=cond_tol)
         if P isa HPolyhedron
             error("linear maps for polyhedra need to be invertible")
         end
diff --git a/src/LinearMap.jl b/src/LinearMap.jl
index 29bfe15d1c..0b4d156371 100644
--- a/src/LinearMap.jl
+++ b/src/LinearMap.jl
@@ -201,13 +201,15 @@ function ρ(d::AbstractVector{N}, lm::LinearMap{N}; kwargs...) where {N<:Real}
 end
 
 """
-    isbounded(lm::LinearMap)::Bool
+    isbounded(lm::LinearMap; cond_tol::Number=DEFAULT_COND_TOL)::Bool
 
 Determine whether a linear map is bounded.
 
 ### Input
 
-- `lm` -- linear map
+- `lm`       -- linear map
+- `cond_tol` -- (optional) tolerance of matrix condition (used to check whether
+                the matrix is invertible)
 
 ### Output
 
@@ -221,11 +223,11 @@ If the matrix is invertible, then the map being bounded is equivalent to the
 wrapped set being bounded, and hence the map is unbounded.
 Otherwise, we check boundedness via [`isbounded_unit_dimensions`](@ref).
 """
-function isbounded(lm::LinearMap)::Bool
+function isbounded(lm::LinearMap; cond_tol::Number=DEFAULT_COND_TOL)::Bool
     if iszero(lm.M) || isbounded(lm.X)
         return true
     end
-    if isinvertible(lm.M)
+    if isinvertible(lm.M; cond_tol=cond_tol)
         return false
     end
     return isbounded_unit_dimensions(lm)
diff --git a/src/helper_functions.jl b/src/helper_functions.jl
index aeb285f4fc..e76066ac30 100644
--- a/src/helper_functions.jl
+++ b/src/helper_functions.jl
@@ -1,3 +1,6 @@
+# default tolerance for matrix condition number (see 'isinvertible')
+DEFAULT_COND_TOL = 1e6
+
 """
     sign_cadlag(x::N)::N where {N<:Real}
 
@@ -87,14 +90,15 @@ function ispermutation(u::AbstractVector{T}, v::AbstractVector{T})::Bool where T
 end
 
 """
-    isinvertible(M::AbstractMatrix; [cond_tol]::Number=1e6)
+    isinvertible(M::AbstractMatrix; [cond_tol]::Number=DEFAULT_COND_TOL)
 
 A sufficient check of a matrix being invertible (or nonsingular).
 
 ### Input
 
 - `M`        -- matrix
-- `cond_tol` -- (optional, default: `1e6`) tolerance of matrix condition
+- `cond_tol` -- (optional, default: `DEFAULT_COND_TOL`) tolerance of matrix
+                condition
 
 ### Output
 
@@ -107,7 +111,7 @@ We check whether the
 [matrix condition number](https://en.wikipedia.org/wiki/Condition_number#Matrices)
 `cond(M)` is below some prescribed tolerance.
 """
-function isinvertible(M::AbstractMatrix; cond_tol::Number=1e6)
+function isinvertible(M::AbstractMatrix; cond_tol::Number=DEFAULT_COND_TOL)
     return cond(M) < cond_tol
 end