diff --git a/Math/LinearMap/Category/Class.hs b/Math/LinearMap/Category/Class.hs
--- a/Math/LinearMap/Category/Class.hs
+++ b/Math/LinearMap/Category/Class.hs
@@ -1824,6 +1824,7 @@
     => VectorSpace (GenericTupleDual f g p)
 instance ( InnerSpace (DualVector (f p)), InnerSpace (DualVector (g p))
          , Scalar (DualVector (f p)) ~ Scalar (DualVector (g p))
+         , AdditiveGroup (Scalar (DualVector (g p)))
          , Num (Scalar (DualVector (f p))) )
     => InnerSpace (GenericTupleDual f g p)
 instance (AdditiveGroup (DualVector (f p)), AdditiveGroup (DualVector (g p)))
@@ -2225,7 +2226,7 @@
                   Coercion -> Coercion
 
 
-instance ∀ s m . ( Num' s
+instance ∀ s m . ( Num s, Num' s
                  , Semimanifold m, LinearSpace (Needle (VRep m))
                  , Scalar (Needle m) ~ s
                  , Scalar (Needle (VRep m)) ~ s )
@@ -2253,7 +2254,7 @@
   coerceDoubleDual = case coerceDoubleDual @(Needle (VRep m)) of
     VSCCoercion -> VSCCoercion
 
-instance ∀ s m . ( Num' s
+instance ∀ s m . ( Num s, Num' s
                  , Semimanifold m
                  , LinearSpace (Needle (VRep m))
                  , TensorSpace (DualVector (Needle (VRep m)))
diff --git a/Math/LinearMap/Category/Instances.hs b/Math/LinearMap/Category/Instances.hs
--- a/Math/LinearMap/Category/Instances.hs
+++ b/Math/LinearMap/Category/Instances.hs
@@ -759,22 +759,26 @@
                  + (asLinearMap$vw)<.>(asLinearMap$vw')
 
 instance ( TensorSpace u, TensorSpace v, TensorSpace w
-         , Num s, Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
+         , AdditiveGroup s, Num s
+         , Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
          , InnerSpace (Tensor s u (Tensor s v w)) )
               => InnerSpace (Tensor s (Tensor s u v) w) where
   s <.> t = (rassocTensor$s)<.>(rassocTensor$t)
 instance ( LinearSpace u, TensorSpace v, TensorSpace w
-         , Num s, Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
+         , AdditiveGroup s, Num s
+         , Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
          , InnerSpace (LinearMap s u (Tensor s v w)) )
               => InnerSpace (Tensor s (LinearMap s u v) w) where
   s <.> t = (hasteLinearMap$s)<.>(hasteLinearMap$t)
 instance ( LinearSpace u, LinearSpace v, TensorSpace w
-         , Num s, Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
+         , AdditiveGroup s, Num s
+         , Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
          , InnerSpace (LinearMap s u (LinearMap s v w)) )
               => InnerSpace (LinearMap s (Tensor s u v) w) where
   s <.> t = (curryLinearMap$s)<.>(curryLinearMap$t)
 instance ( LinearSpace u, LinearSpace v, TensorSpace w
-         , Num s, Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
+         , AdditiveGroup s, Num s
+         , Scalar u ~ s, Scalar v ~ s, Scalar w ~ s
          , InnerSpace (Tensor s u (LinearMap s v w)) )
               => InnerSpace (LinearMap s (LinearMap s u v) w) where
   s <.> t = (coCurryLinearMap$s)<.>(coCurryLinearMap$t)
diff --git a/Math/VectorSpace/Docile.hs b/Math/VectorSpace/Docile.hs
--- a/Math/VectorSpace/Docile.hs
+++ b/Math/VectorSpace/Docile.hs
@@ -1087,6 +1087,9 @@
  where du = subbasisDimension (entireBasis :: SubBasis u)
        dv = subbasisDimension (entireBasis :: SubBasis v)
     
+{-# DEPRECATED (\$) "The current inversion algorithm is wrong in rare edge cases. It is also dubious how useful it is given that 'SimpleSpace' has in practice just Euclidean-isomorphic spaces as instances, for which off-the-shelf matrix inversion could be used. These functions will probably be removed in favour of something e.g. conjugate-gradient based." #-}
+
+{-# DEPRECATED pseudoInverse "The current inversion algorithm is wrong in rare edge cases. It is also dubious how useful it is given that 'SimpleSpace' has in practice just Euclidean-isomorphic spaces as instances, for which off-the-shelf matrix inversion could be used. These functions will probably be removed in favour of something e.g. conjugate-gradient based." #-}
 
 pseudoInverse :: ∀ u v . ( SimpleSpace u, SimpleSpace v, Scalar u ~ Scalar v )
           => (u+>v) -> v+>u
diff --git a/linearmap-category.cabal b/linearmap-category.cabal
--- a/linearmap-category.cabal
+++ b/linearmap-category.cabal
@@ -2,7 +2,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                linearmap-category
-version:             0.6.0.1
+version:             0.6.0.2
 synopsis:            Native, complete-ish, matrix-free linear algebra.
 description:         The term /numerical linear algebra/ is often used almost
                      synonymous with /matrix modifications/. However, what's interesting
@@ -71,27 +71,27 @@
                        Math.VectorSpace.Docile
   other-extensions:    FlexibleInstances, UndecidableInstances, FunctionalDependencies, TypeOperators, TypeFamilies
   build-depends:       base >=4.8 && <5,
-                       vector-space >=0.11 && <0.18, MemoTrie,
+                       vector-space >=0.11 && <0.20, MemoTrie <0.7,
                        constrained-categories >=0.3 && <0.5,
-                       containers,
+                       containers <0.9,
                        vector >=0.12 && <0.14,
-                       tagged,
+                       tagged <0.9,
                        free-vector-spaces >= 0.1.4 && < 0.3,
-                       linear, lens, transformers,
+                       linear <1.24, lens <5.4, transformers <0.7,
                        manifolds-core >= 0.6.1.0 && < 0.7,
-                       semigroups, hashable,
-                       data-default-class,
+                       semigroups <0.21, hashable <1.6,
+                       data-default-class <0.3,
                        ieee754 >= 0.7 && < 0.9,
-                       call-stack,
-                       template-haskell >=2.12 && <2.21,
-                       th-abstraction >=0.4 && <0.6,
+                       call-stack <0.5,
+                       template-haskell >=2.12 && <2.24,
+                       th-abstraction >=0.4 && <0.8,
                        ghc-typelits-natnormalise >=0.7 && <0.8,
                        type-natural >=1.0 && <1.4,
-                       QuickCheck >=2.11 && <2.15
+                       QuickCheck >=2.15 && <2.16
   if flag(singletons3)
     build-depends:
                        singletons >=3.0 && <3.3,
-                       singletons-base >=3.0 && <3.3
+                       singletons-base >=3.0 && <3.5
   else
     build-depends:
                        singletons >=2.7 && <3.0
@@ -107,7 +107,7 @@
                    , manifolds-core
                    , linear, vector
                    , constrained-categories
-                   , tasty, tasty-quickcheck
+                   , tasty <1.6, tasty-quickcheck <0.12
   ghc-options: -threaded "-with-rtsopts -N8 -M2G"
   default-language:    Haskell2010
 
diff --git a/test/tasty/test.hs b/test/tasty/test.hs
--- a/test/tasty/test.hs
+++ b/test/tasty/test.hs
@@ -143,9 +143,10 @@
    [ testGroup "Euclidean space"
     [ testProperty "co-Riesz inversion"
      $ \v -> (arr coRiesz\$coRiesz-+$>v) === (v :: V4 ℝ)
-    , testProperty "Random operator inversion"      -- This isn't really expected to work
-     $ \f v -> (f \$ (f :: V4 ℝ+>V4 ℝ) $ v) ≈≈≈ v   -- /always/, but singular matrices are
-    ]                                               -- very seldom in the @Arbitrary@ instance.
+--  , testProperty "Random operator inversion"
+--   $ \f v -> not (isSingular f)
+--            ==> (f \$ (f :: V4 ℝ+>V4 ℝ) $ v) ≈≈≈ v
+    ]
    , testGroup "Basis-derived space"
     [ testProperty "Semimanifold addition"
      $ \v w -> v.+~^w === (v^+^w :: ℝ⁵ Int)
@@ -237,6 +238,10 @@
 v≈≈≈w
  | magnitudeSq (v^-^w) < (magnitudeSq v + magnitudeSq w)*1e-8   = QC.property True
  | otherwise                                                    = v===w
+
+isSingular :: ∀ v n . (n`Dimensional`v, Scalar v ~ ℝ)
+             => (v +> v) -> Bool
+isSingular _ = undefined
 
 uar :: UArr.Unbox a => [a] -> UArr.Vector a
 uar = UArr.fromList