diff --git a/Project.toml b/Project.toml
index 31c9281f..705d0bb1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "ManifoldsBase"
 uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
 authors = ["Seth Axen <seth.axen@gmail.com>", "Mateusz Baran <mateuszbaran89@gmail.com>", "Ronny Bergmann <manopt@ronnybergmann.net>", "Antoine Levitt <antoine.levitt@gmail.com>"]
-version = "0.8.0"
+version = "0.8.1"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/EmbeddedManifold.jl b/src/EmbeddedManifold.jl
index 9a27feb1..41898a9d 100644
--- a/src/EmbeddedManifold.jl
+++ b/src/EmbeddedManifold.jl
@@ -6,7 +6,7 @@ A type used to specify properties of an [`AbstractEmbeddedManifold`](@ref).
 abstract type AbstractEmbeddingType end
 
 """
-    AbstractEmbeddedManifold{T<:AbstractEmbeddingType,𝔽} <: AbstractDecoratorManifold{𝔽}
+    AbstractEmbeddedManifold{𝔽,T<:AbstractEmbeddingType,𝔽} <: AbstractDecoratorManifold{𝔽}
 
 An abstract type for embedded manifolds, which acts as an [`AbstractDecoratorManifold`](@ref).
 The functions of the manifold that is embedded can hence be just passed on to the embedding.
@@ -20,7 +20,7 @@ abstract type AbstractEmbeddedManifold{𝔽,T<:AbstractEmbeddingType} <:
               AbstractDecoratorManifold{𝔽} end
 
 """
-DefaultEmbeddingType <: AbstractEmbeddingType
+    DefaultEmbeddingType <: AbstractEmbeddingType
 
 A type of default embedding that does not have any special properties.
 """
diff --git a/src/ManifoldsBase.jl b/src/ManifoldsBase.jl
index 18d4c151..63fed2cf 100644
--- a/src/ManifoldsBase.jl
+++ b/src/ManifoldsBase.jl
@@ -737,8 +737,9 @@ shortest_geodesic(M::Manifold, p, q, T::AbstractVector) = geodesic(M, p, log(M,
     vector_transport_along(M::Manifold, p, X, c)
     vector_transport_along(M::Manifold, p, X, c, method::AbstractVectorTransportMethod)
 
-Transport a vector `X` from a point `p` along the curve `c` such that `c(0)` is equal to `p`
-to the point `c(1)` using the `method`, which defaults to [`ParallelTransport`](@ref).
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+along the curve `c` such that `c(0)` is equal to `p` to the point `c(1)` using the `method`,
+which defaults to [`ParallelTransport`](@ref).
 """
 function vector_transport_along(M::Manifold, p, X, c)
     return vector_transport_along(M, p, X, c, ParallelTransport())
@@ -753,9 +754,9 @@ end
     vector_transport_along!(M::Manifold, Y, p, X, c)
     vector_transport_along!(M::Manifold, Y, p, X, c, method::AbstractVectorTransportMethod)
 
-Transport a vector `X` from a point `p` along the curve `c` such that `c(0)` is equal to `p`
-to the point `c(1)` using the `method`, which defaults to [`ParallelTransport`](@ref).
-The result is saved to `Y`.
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+along the curve `c` such that `c(0)` is equal to `p` to the point `c(1)` using the `method`,
+which defaults to [`ParallelTransport`](@ref). The result is saved to `Y`.
 """
 function vector_transport_along!(M::Manifold, Y, p, X, c)
     return vector_transport_along!(M, Y, p, X, c, ParallelTransport())
@@ -785,9 +786,10 @@ end
     vector_transport_direction(M::Manifold, p, X, d)
     vector_transport_direction(M::Manifold, p, X, d, method::AbstractVectorTransportMethod)
 
-Transport a vector `X` from a point `p` in the direction indicated by the tangent vector `d`
-at point `p`. By default, [`exp`](@ref) and [`vector_transport_to!`](@ref) are used with
-the `method`, which defaults to [`ParallelTransport`](@ref).
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+in the direction indicated by the tangent vector `d` at `p`. By default, [`exp`](@ref) and
+[`vector_transport_to!`](@ref) are used with the `method`, which defaults
+to [`ParallelTransport`](@ref).
 """
 function vector_transport_direction(M::Manifold, p, X, d)
     return vector_transport_direction(M, p, X, d, ParallelTransport())
@@ -808,10 +810,10 @@ end
     vector_transport_direction!(M::Manifold, Y, p, X, d)
     vector_transport_direction!(M::Manifold, Y, p, X, d, method::AbstractVectorTransportMethod)
 
-Transport a vector `X` from a point `p` in the direction indicated by the tangent vector `d`
-at point `p`. The result is saved to `Y`. By default, [`exp`](@ref) and
-[`vector_transport_to!`](@ref) are used with the `method`, which defaults to
-[`ParallelTransport`](@ref).
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+in the direction indicated by the tangent vector `d` at `p`. By default, [`exp`](@ref) and
+[`vector_transport_to!`](@ref) are used with the `method`, which defaults
+to [`ParallelTransport`](@ref). The result is saved to `Y`.
 """
 function vector_transport_direction!(M::Manifold, Y, p, X, d)
     return vector_transport_direction!(M, Y, p, X, d, ParallelTransport())
@@ -832,7 +834,8 @@ end
     vector_transport_to(M::Manifold, p, X, q)
     vector_transport_to(M::Manifold, p, X, q, method::AbstractVectorTransportMethod)
 
-Compute the vector transport of vector `X` at point `p` to point `q`.
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+along the [`shortest_geodesic`](@ref) to the tangent space at another point `q`.
 By default, the [`AbstractVectorTransportMethod`](@ref) `method` is
 [`ParallelTransport`](@ref).
 """
@@ -849,9 +852,10 @@ end
     vector_transport_to!(M::Manifold, Y, p, X, q)
     vector_transport_to!(M::Manifold, Y, p, X, q, method::AbstractVectorTransportMethod)
 
-Compute the vector transport of vector `X` at point `p` to point `q`.
-The result is saved to `Y`. By default, the [`AbstractVectorTransportMethod`](@ref) `method`
-is [`ParallelTransport`](@ref).
+Transport a vector `X` from the tangent space at a point `p` on the [`Manifold`](@ref) `M`
+along the [`shortest_geodesic`](@ref) to the tangent space at another point `q`.
+By default, the [`AbstractVectorTransportMethod`](@ref) `method` is
+[`ParallelTransport`](@ref). The result is saved to `Y`.
 """
 function vector_transport_to!(M::Manifold, Y, p, q, X)
     return vector_transport_to!(M, Y, p, q, X, ParallelTransport())
@@ -859,9 +863,9 @@ end
 """
     vector_transport_to!(M::Manifold, Y, p, X, q, method::ProjectionTransport)
 
-Transport a vector `X` from the tangent space at `p` on a [`Manifold`](@ref) `M` by
+Transport a vector `X` from the tangent space at `p` on the [`Manifold`](@ref) `M` by
 interpreting it as an element of the embedding and then projecting it onto the tangent space
-at `q`. This method requires [`project`](@ref).
+at `q`. This method requires  [`project`](@ref project(M::Manifold, p, X)).
 """
 function vector_transport_to!(M::Manifold, Y, p, X, q, ::ProjectionTransport)
     return project!(M, Y, q, X)
@@ -977,6 +981,7 @@ export allocate,
     manifold_dimension,
     norm,
     number_eltype,
+    number_of_coordinates,
     number_system,
     project,
     project!,
diff --git a/src/ValidationManifold.jl b/src/ValidationManifold.jl
index 9c553d31..e7038c68 100644
--- a/src/ValidationManifold.jl
+++ b/src/ValidationManifold.jl
@@ -1,13 +1,13 @@
 """
-    ValidationManifold{M<:Manifold} <: Manifold
+    ValidationManifold{𝔽,M<:Manifold{𝔽}} <: AbstractDecoratorManifold{𝔽}
 
-A manifold to encapsulate manifolds working on array representations of `MPoints` and
-`TVectors` in a transparent way, such that for these manifolds it's not necessary to
-introduce explicit types for the points and tangent vectors, but they are
+A manifold to encapsulate manifolds working on array representations of [`MPoint`](@ref)s
+and [`TVector`](@ref)s in a transparent way, such that for these manifolds it's not
+necessary to introduce explicit types for the points and tangent vectors, but they are
 encapsulated/stripped automatically when needed.
 
-This manifold is a decorator for a manifold, i.e. it decorates a manifold `M` with types
-points, vectors, and covectors.
+This manifold is a decorator for a manifold, i.e. it decorates a [`Manifold`](@ref) `M`
+with types points, vectors, and covectors.
 """
 struct ValidationManifold{𝔽,M<:Manifold{𝔽}} <: AbstractDecoratorManifold{𝔽}
     manifold::M
@@ -183,7 +183,8 @@ function get_basis(
     kwargs...,
 ) where {𝔽}
     is_manifold_point(M, p, true; kwargs...)
-    Ξ = invoke(get_basis, Tuple{ValidationManifold,Any,AbstractOrthogonalBasis}, M, p, B; kwargs...)
+    get_basis_invoke_types = Tuple{ValidationManifold,Any,Union{AbstractOrthogonalBasis,CachedBasis{𝔽,<:AbstractOrthogonalBasis{𝔽}}} where {𝔽}}
+    Ξ = invoke(get_basis, get_basis_invoke_types, M, p, B; kwargs...)
     bvectors = get_vectors(M, p, Ξ)
     N = length(bvectors)
     for i = 1:N
diff --git a/src/bases.jl b/src/bases.jl
index fbd5d4e1..4ba22d00 100644
--- a/src/bases.jl
+++ b/src/bases.jl
@@ -117,8 +117,8 @@ struct DiagonalizingBasisData{D,V,ET}
     vectors::V
 end
 
-const DefaultOrDiagonalizingBasis =
-    Union{DefaultOrthonormalBasis,DiagonalizingOrthonormalBasis}
+const DefaultOrDiagonalizingBasis{𝔽} =
+    Union{DefaultOrthonormalBasis{𝔽},DiagonalizingOrthonormalBasis{𝔽}}
 
 """
     CachedBasis{𝔽,V,<:AbstractBasis{𝔽}} <: AbstractBasis{𝔽}
@@ -156,10 +156,6 @@ function get_vector end
 const all_uncached_bases = Union{AbstractBasis, DefaultBasis, DefaultOrthogonalBasis, DefaultOrthonormalBasis}
 const DISAMBIGUATION_BASIS_TYPES = [
     CachedBasis,
-    CachedBasis{ℝ,<:AbstractBasis{ℝ}},
-    CachedBasis{ℂ,<:AbstractBasis{ℂ}},
-    CachedBasis{ℝ,<:AbstractOrthogonalBasis{ℝ}},
-    CachedBasis{ℝ,<:AbstractOrthonormalBasis{ℝ}},
     DefaultBasis,
     DefaultOrthonormalBasis,
     DefaultOrthogonalBasis,
@@ -169,14 +165,20 @@ const DISAMBIGUATION_BASIS_TYPES = [
     VeeOrthogonalBasis,
 ]
 
-function allocate_result(M::Manifold, f::typeof(get_coordinates), p, X, B)
+function allocate_result(
+    M::Manifold,
+    f::typeof(get_coordinates),
+    p,
+    X,
+    B::AbstractBasis,
+)
     T = allocate_result_type(M, f, (p, X))
-    return allocate(p, T, manifold_dimension(M))
+    return allocate(p, T, number_of_coordinates(M, B))
 end
 
 function allocate_result(M::Manifold, f::typeof(get_coordinates), p, X, B::CachedBasis)
     T = allocate_result_type(M, f, (p, X))
-    return allocate(p, T, length(get_vectors(M, p, B)))
+    return allocate(p, T, number_of_coordinates(M, B))
 end
 
 @inline function allocate_result_type(
@@ -229,6 +231,10 @@ See also: [`get_coordinates`](@ref), [`get_vector`](@ref)
 function get_basis(M::Manifold, p, B::AbstractBasis)
     error("get_basis not implemented for manifold of type $(typeof(M)) a point of type $(typeof(p)) and basis of type $(typeof(B)).")
 end
+@decorator_transparent_signature get_basis(M::AbstractDecoratorManifold, p, B::AbstractBasis)
+function decorator_transparent_dispatch(::typeof(get_basis), ::Manifold, args...)
+    return Val(:parent)
+end
 
 function get_basis(M::Manifold, p, B::DefaultOrthonormalBasis)
     dim = manifold_dimension(M)
@@ -305,6 +311,11 @@ function get_basis(
         error("get_basis with bases $(typeof(B)) only found $(K) orthonormal basis vectors, but manifold dimension is $(dim).")
     end
 end
+for BT in DISAMBIGUATION_BASIS_TYPES
+    eval(quote
+        @decorator_transparent_signature get_basis(M::AbstractDecoratorManifold, p, B::$BT)
+    end)
+end
 
 """
     get_coordinates(M::Manifold, p, X, B::AbstractBasis)
@@ -354,11 +365,14 @@ end
 function get_coordinates!(M::Manifold, Y, p, X, B::DefaultOrthogonalBasis)
     return get_coordinates!(M, Y, p, X, DefaultOrthonormalBasis(number_system(B)))
 end
-function get_coordinates!(M::Manifold{𝔾}, Y, p, X, C::CachedBasis{𝔽,B,V}) where {B,V,𝔾,𝔽}
-    map!(vb -> conj(inner(M, p, X, vb)), Y, get_vectors(M, p, C))
+function get_coordinates!(M::Manifold, Y, p, X, B::CachedBasis)
+    _get_coordinates!(M, number_system(M), Y, p, X, B, number_system(B))
+end
+function _get_coordinates!(M::Manifold, ::ComplexNumbers, Y, p, X, B::CachedBasis,::RealNumbers)
+    map!(vb -> conj(inner(M, p, X, vb)), Y, get_vectors(M, p, B))
     return Y
 end
-function get_coordinates!(M::Manifold{𝔽}, Y, p, X, C::CachedBasis{𝔽,B,V}) where {B,V,𝔽}
+function _get_coordinates!(M::Manifold, a::𝔽, Y, p, X, C::CachedBasis, b::𝔽) where {𝔽}
     map!(vb -> real(inner(M, p, X, vb)), Y, get_vectors(M, p, C))
     return Y
 end
@@ -417,6 +431,7 @@ function get_vector!(M::Manifold, Y, p, X, B::CachedBasis)
     #  2) guarantees a reasonable array type `Y`
     #     (for example scalar * `SizedValidation` is an `SArray`)
     bvectors = get_vectors(M, p, B)
+    #print("hi.\nB:$(B)\n& X:$(X)\n\nyields\n $(bvectors).")
     if _get_vector_cache_broadcast(bvectors[1]) === Val(false)
         Xt = X[1] * bvectors[1]
         copyto!(Y, Xt)
@@ -471,6 +486,20 @@ inverse.
 hat(M::Manifold, p, X) = get_vector(M, p, X, VeeOrthogonalBasis())
 hat!(M::Manifold, Y, p, X) = get_vector!(M, Y, p, X, VeeOrthogonalBasis())
 
+"""
+    number_of_coordinates(M::Manifold, B::AbstractBasis)
+
+Compute the number of coordinates in basis `B` of manifold `M`.
+This also corresponds to the number of vectors represented by `B`,
+or stored within `B` in case of a [`CachedBasis`](@ref).
+"""
+function number_of_coordinates(M::Manifold{𝔽}, B::AbstractBasis{𝔾}) where {𝔽,𝔾}
+    return div(manifold_dimension(M), real_dimension(𝔽)) * real_dimension(𝔾)
+end
+function number_of_coordinates(M::Manifold{𝔽}, B::AbstractBasis{𝔽}) where {𝔽}
+   return manifold_dimension(M)
+end
+
 """
     number_system(::AbstractBasis)
 
diff --git a/src/numbers.jl b/src/numbers.jl
index 2acc663f..6179d5de 100644
--- a/src/numbers.jl
+++ b/src/numbers.jl
@@ -9,6 +9,7 @@ the fields [`RealNumbers`](@ref) (`ℝ` for short) and [`ComplexNumbers`](@ref)
 abstract type AbstractNumbers end
 
 """
+    RealNumbers <: AbstractNumbers
     ℝ = RealNumbers()
 
 The field of real numbers.
@@ -16,6 +17,7 @@ The field of real numbers.
 struct RealNumbers <: AbstractNumbers end
 
 """
+    ComplexNumbers <: AbstractNumbers
     ℂ = ComplexNumbers()
 
 The field of complex numbers.
@@ -23,6 +25,7 @@ The field of complex numbers.
 struct ComplexNumbers <: AbstractNumbers end
 
 """
+    QuaternionNumbers <: AbstractNumbers
     ℍ = QuaternionNumbers()
 
 The division algebra of quaternions.
@@ -33,6 +36,26 @@ const ℝ = RealNumbers()
 const ℂ = ComplexNumbers()
 const ℍ = QuaternionNumbers()
 
+"""
+    _unify_number_systems(𝔽s::AbstractNumbers...)
+
+Compute a number system that includes all given number systems (as sub-systems) and is
+closed under addition and multiplication.
+"""
+function _unify_number_systems(a::AbstractNumbers, rest::AbstractNumbers...)
+    return _unify_number_systems(a, _unify_number_systems(rest...))
+end
+_unify_number_systems(𝔽::AbstractNumbers) = 𝔽
+_unify_number_systems(r::RealNumbers, ::RealNumbers) = r
+_unify_number_systems(::RealNumbers, c::ComplexNumbers) = c
+_unify_number_systems(::RealNumbers, q::QuaternionNumbers) = q
+_unify_number_systems(c::ComplexNumbers, ::RealNumbers) = c
+_unify_number_systems(c::ComplexNumbers, ::ComplexNumbers) = c
+_unify_number_systems(::ComplexNumbers, q::QuaternionNumbers) = q
+_unify_number_systems(q::QuaternionNumbers, ::RealNumbers) = q
+_unify_number_systems(q::QuaternionNumbers, ::ComplexNumbers) = q
+_unify_number_systems(q::QuaternionNumbers, ::QuaternionNumbers) = q
+
 Base.show(io::IO, ::RealNumbers) = print(io, "ℝ")
 Base.show(io::IO, ::ComplexNumbers) = print(io, "ℂ")
 Base.show(io::IO, ::QuaternionNumbers) = print(io, "ℍ")
@@ -40,7 +63,7 @@ Base.show(io::IO, ::QuaternionNumbers) = print(io, "ℍ")
 @doc raw"""
     real_dimension(𝔽::AbstractNumbers)
 
-Return the real dimension $\dim_ℝ 𝔽$ of the [`AbstractNumbers`] system `𝔽`.
+Return the real dimension $\dim_ℝ 𝔽$ of the [`AbstractNumbers`](@ref) system `𝔽`.
 The real dimension is the dimension of a real vector space with which a number in `𝔽` can be
 identified.
 For example, [`ComplexNumbers`](@ref) have a real dimension of 2, and
diff --git a/test/bases.jl b/test/bases.jl
index bf420f84..52617566 100644
--- a/test/bases.jl
+++ b/test/bases.jl
@@ -13,6 +13,12 @@ ManifoldsBase.manifold_dimension(::ProjManifold) = 5
 ManifoldsBase.get_vector(::ProjManifold, x, v, ::DefaultOrthonormalBasis) = reverse(v)
 
 @testset "Dispatch" begin
+    @test ManifoldsBase.decorator_transparent_dispatch(
+        get_basis,
+        DefaultManifold(3),
+        [0.0, 0.0, 0.0],
+        DefaultBasis(),
+    ) === Val(:parent)
     @test ManifoldsBase.decorator_transparent_dispatch(
         get_coordinates,
         DefaultManifold(3),
@@ -200,6 +206,7 @@ DiagonalizingBasisProxy() = DiagonalizingOrthonormalBasis([1.0, 0.0, 0.0])
             continue
         end
         v1 = log(M, pts[1], pts[2])
+        @test ManifoldsBase.number_of_coordinates(M, BT()) == 3
 
         if BT != DiagonalizingBasisProxy
             vb = get_coordinates(M, pts[1], v1, BT())
@@ -259,15 +266,17 @@ end
     X = [1.2, 2.2im, 2.3im]
     b = [Matrix{Float64}(I,3,3)[:,i] for i=1:3]
     Bℝ = CachedBasis(DefaultOrthonormalBasis{ℝ}(),b)
-    aℝ = get_coordinates(M,p,X,Bℝ)
-    Yℝ = get_vector(M,p,aℝ,Bℝ)
+    aℝ = get_coordinates(M, p, X, Bℝ)
+    Yℝ = get_vector(M, p, aℝ, Bℝ)
     @test Yℝ ≈ X
+    @test ManifoldsBase.number_of_coordinates(M, Bℝ) == 3
 
     bℂ = [b...,(b.*1im)...]
     Bℂ = CachedBasis(DefaultOrthonormalBasis{ℂ}(), bℂ)
-    aℂ = get_coordinates(M,p,X,Bℂ)
-    Yℂ = get_vector(M,p,aℂ,Bℂ)
+    aℂ = get_coordinates(M, p, X, Bℂ)
+    Yℂ = get_vector(M, p, aℂ, Bℂ)
     @test Yℂ ≈ X
+    @test ManifoldsBase.number_of_coordinates(M, Bℂ) == 6
 end
 
 @testset "Basis show methods" begin
diff --git a/test/numbers.jl b/test/numbers.jl
index ee22607c..ff87ec10 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -1,6 +1,6 @@
 using Test
 using ManifoldsBase
-using ManifoldsBase: AbstractNumbers, ℝ, ℂ, ℍ
+using ManifoldsBase: AbstractNumbers, ℝ, ℂ, ℍ, _unify_number_systems
 
 struct NotImplementedNumbers <: ManifoldsBase.AbstractNumbers end
 
@@ -21,4 +21,19 @@ struct NotImplementedNumbers <: ManifoldsBase.AbstractNumbers end
     @test ManifoldsBase.QuaternionNumbers() === ℍ
     @test real_dimension(ℍ) == 4
     @test repr(ℍ) == "ℍ"
+
+    @test (@inferred _unify_number_systems(ℝ)) === ℝ
+    @test (@inferred _unify_number_systems(ℂ)) === ℂ
+    @test (@inferred _unify_number_systems(ℍ)) === ℍ
+    @test (@inferred _unify_number_systems(ℝ, ℝ)) === ℝ
+    @test (@inferred _unify_number_systems(ℝ, ℂ)) === ℂ
+    @test (@inferred _unify_number_systems(ℝ, ℍ)) === ℍ
+    @test (@inferred _unify_number_systems(ℂ, ℝ)) === ℂ
+    @test (@inferred _unify_number_systems(ℂ, ℂ)) === ℂ
+    @test (@inferred _unify_number_systems(ℂ, ℍ)) === ℍ
+    @test (@inferred _unify_number_systems(ℍ, ℝ)) === ℍ
+    @test (@inferred _unify_number_systems(ℍ, ℂ)) === ℍ
+    @test (@inferred _unify_number_systems(ℍ, ℍ)) === ℍ
+    @test (@inferred _unify_number_systems(ℝ, ℂ, ℝ)) === ℂ
+    @test (@inferred _unify_number_systems(ℝ, ℝ, ℝ)) === ℝ
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 077d3460..8dcd2605 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,9 +1,10 @@
 using Test
 using ManifoldsBase
-
 @testset "ManifoldsBase" begin
-    # This should remain at 0
-    @test length(Test.detect_ambiguities(ManifoldsBase)) == 0
+
+    num_ambiguities = length(Test.detect_ambiguities(ManifoldsBase))
+    #num_ambiguities > 0 && @warn "The number of ambiguities in ManifoldsBase is $(num_ambiguities)."
+    @test num_ambiguities == 0
     include("allocation.jl")
     include("numbers.jl")
     include("bases.jl")
diff --git a/test/validation_manifold.jl b/test/validation_manifold.jl
index 938514c4..5f2cfaf2 100644
--- a/test/validation_manifold.jl
+++ b/test/validation_manifold.jl
@@ -142,9 +142,9 @@ end
                 @test_throws ErrorException get_basis(A, x, CachedBasis(cb, [x, x, x]))
                 @test_throws ErrorException get_basis(A, x, CachedBasis(cb, [2*x, x, x]))
                 if BT <: ManifoldsBase.AbstractOrthogonalBasis
-                    @test_throws ErrorException get_basis(A, x, CachedBasis(cb, [[1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
+                    @test_throws ArgumentError get_basis(A, x, CachedBasis(cb, [[1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
                 elseif BT <: ManifoldsBase.AbstractOrthonormalBasis
-                    @test_throws ErrorException get_basis(A, x, CachedBasis(cb, [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
+                    @test_throws ArgumentError get_basis(A, x, CachedBasis(cb, [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
                 end
             end
         end