diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,8 @@
 # Changelog for linear-tests
 
+## 0.1.2 [2020.03.27]
+- Added `NonZeroV3` and `NonZeroV4`
+
 ## 0.1.1 [2020.02.16]
 - Added `InvertibleM33`
 - Added `BasisV3`
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,8 +1,6 @@
-[![CircleCI](https://circleci.com/gh/pdlla/linear-tests.svg?style=svg)](https://circleci.com/gh/pdlla/linear-tests)
-
 # linear-tests
 This library provides [QuickCheck](https://hackage.haskell.org/package/QuickCheck) `Arbitrary` instances of data types in the [linear](http://hackage.haskell.org/package/linear) package.
 
 The property tests in this package test both the newly defined `Arbitrary` instances as well as methods in the linear package itself. It's hard to distinguish between the two types of test so they are all just lumped together.
 
-The current instances are just ones I (and hopefully others) find useful. Feel free to add your own and submit a PR. 
+The current instances are just ones I (and hopefully others) find useful. Feel free to add your own and submit a PR.
diff --git a/linear-tests.cabal b/linear-tests.cabal
--- a/linear-tests.cabal
+++ b/linear-tests.cabal
@@ -4,10 +4,10 @@
 --
 -- see: https://github.com/sol/hpack
 --
--- hash: 7d0fbb63b1f76fdccf74b6a953e18091d9a95568447c823ca6244cc4a413b720
+-- hash: a47f9bb7aa67c051f663274d346bb9eccfcd437b97b8bf43dc8420896c5c4b20
 
 name:           linear-tests
-version:        0.1.1.0
+version:        0.1.2.0
 synopsis:       Linear Algebra
 description:    Please see the README on GitHub at <https://github.com/pdlla/linear-tests#readme>
 category:       Math, Algebra, Testing
diff --git a/src/Linear/Matrix/Arbitrary.hs b/src/Linear/Matrix/Arbitrary.hs
--- a/src/Linear/Matrix/Arbitrary.hs
+++ b/src/Linear/Matrix/Arbitrary.hs
@@ -12,7 +12,6 @@
 
 import           Linear.Epsilon
 import           Linear.Matrix
-import           Linear.Metric
 import qualified Linear.V3           as V3
 import qualified Linear.V4           as V4
 import           Test.QuickCheck
diff --git a/src/Linear/V3/Arbitrary.hs b/src/Linear/V3/Arbitrary.hs
--- a/src/Linear/V3/Arbitrary.hs
+++ b/src/Linear/V3/Arbitrary.hs
@@ -2,16 +2,13 @@
 
 module Linear.V3.Arbitrary (
   UnitV3(..)
+  , NonZeroV3(..)
   , CartesianUnitV3(..)
   , BasisV3(..)
 ) where
 
-import           Control.Lens      hiding (elements)
-
-import           Linear.Conjugate
 import           Linear.Epsilon
 import           Linear.Metric
-import qualified Linear.Quaternion as Q
 import           Linear.V3
 import           Linear.Vector
 
@@ -20,6 +17,14 @@
 -- | `Arbitrary V3` has no restrictions on components
 instance (Arbitrary a) => Arbitrary (V3 a) where
   arbitrary = V3 <$> arbitrary <*> arbitrary <*> arbitrary
+
+-- | `Arbitrary NonZero` is never the zero vector
+newtype NonZeroV3 a = NonZeroV3 {unNonZeroV3 :: V3 a} deriving (Show)
+
+instance (Arbitrary a, Epsilon a, Floating a) => Arbitrary (NonZeroV3 a) where
+  arbitrary = do
+    v <- arbitrary `suchThat` (not . nearZero)
+    return $ NonZeroV3 v
 
 -- | `Arbitrary UnitV3` always has norm 1
 newtype UnitV3 a = UnitV3 {unUnitV3 :: V3 a}  deriving (Show)
diff --git a/src/Linear/V4/Arbitrary.hs b/src/Linear/V4/Arbitrary.hs
--- a/src/Linear/V4/Arbitrary.hs
+++ b/src/Linear/V4/Arbitrary.hs
@@ -2,6 +2,7 @@
 
 module Linear.V4.Arbitrary (
   UnitV4(..)
+  , NonZeroV4(..)
 ) where
 
 import           Linear.Epsilon
@@ -13,6 +14,14 @@
 -- | `Arbitrary V4` has no restrictions on components
 instance (Arbitrary a) => Arbitrary (V4 a) where
   arbitrary = V4 <$> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
+
+-- | `Arbitrary NonZero` is never the zero vector
+newtype NonZeroV4 a = NonZeroV4 {unNonZeroV4 :: V4 a} deriving (Show)
+
+instance (Arbitrary a, Epsilon a, Floating a) => Arbitrary (NonZeroV4 a) where
+  arbitrary = do
+    v <- arbitrary `suchThat` (not . nearZero)
+    return $ NonZeroV4 v
 
 -- | `Arbitrary UnitV4` always has norm 1
 newtype UnitV4 a = UnitV4 {unUnitV4 :: V4 a}  deriving (Show)
diff --git a/test/Linear/QuaternionSpec.hs b/test/Linear/QuaternionSpec.hs
--- a/test/Linear/QuaternionSpec.hs
+++ b/test/Linear/QuaternionSpec.hs
@@ -33,8 +33,8 @@
 prop_Quaternion_conjugate :: (Epsilon a, RealFloat a, Conjugate a) => Q.Quaternion a -> Bool
 prop_Quaternion_conjugate q = nearZero $ distance (q * conjugate q) (Q.Quaternion 1 (V.V3 0 0 0))
 
-identityQuaternion :: (RealFloat a) => Q.Quaternion a
-identityQuaternion = 1 -- Quaternion 1 (V3 0 0 0)
+--identityQuaternion :: (RealFloat a) => Q.Quaternion a
+--identityQuaternion = 1 -- Quaternion 1 (V3 0 0 0)
 
 spec :: Spec
 spec = specTyped @Double
diff --git a/test/Linear/V3Spec.hs b/test/Linear/V3Spec.hs
--- a/test/Linear/V3Spec.hs
+++ b/test/Linear/V3Spec.hs
@@ -17,6 +17,10 @@
 
 import           Linear.V3.Arbitrary
 
+-- | test for the property `|v| != 0`
+prop_NonZeroV3_isNonZero :: (Epsilon a, Floating a) => NonZeroV3 a -> Bool
+prop_NonZeroV3_isNonZero (NonZeroV3 v) = not . nearZero $ norm v
+
 -- | test for the property `|v| = 1`
 prop_UnitV3_isUnit :: (Epsilon a, Floating a) => UnitV3 a -> Bool
 prop_UnitV3_isUnit (UnitV3 v) = nearZero $ norm v - 1
@@ -53,6 +57,9 @@
 specTyped = do
   describe "V3" $ do
     describe "Arbitrary" $ do
+      describe "NonZeroV3" $ do
+        it "satisfies the property `|v| != 0`" $ do
+          property $ prop_NonZeroV3_isNonZero @a
       describe "UnitV3" $ do
         it "satisfies the property `|v| = 1`" $ do
           property $ prop_UnitV3_isUnit @a
diff --git a/test/Linear/V4Spec.hs b/test/Linear/V4Spec.hs
--- a/test/Linear/V4Spec.hs
+++ b/test/Linear/V4Spec.hs
@@ -17,6 +17,10 @@
 import           Linear.V4.Arbitrary
 
 
+-- | test for the property `|v| != 0`
+prop_NonZeroV4_isNonZero :: (Epsilon a, Floating a) => NonZeroV4 a -> Bool
+prop_NonZeroV4_isNonZero (NonZeroV4 v) = not . nearZero $ norm v
+
 -- | test for the property `|v| = 1`
 prop_UnitV4_isUnit :: (Epsilon a, Floating a) => UnitV4 a -> Bool
 prop_UnitV4_isUnit (UnitV4 v) = nearZero $ norm v - 1
@@ -28,6 +32,9 @@
 specTyped = do
   describe "V4" $ do
     describe "Arbitrary" $ do
+      describe "NonZeroV4" $ do
+        it "satisfies the property `|v| != 0`" $ do
+          property $ prop_NonZeroV4_isNonZero @a
       describe "UnitV4" $ do
         it "satisfies the property `|v| = 1`" $ do
           property $ prop_UnitV4_isUnit @a