diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,5 +4,3 @@
   - mkdir -p ~/.cabal
   - cp config ~/.cabal/config
   - cabal update
-notifications:
-  irc: "irc.freenode.org#haskell-lens"
diff --git a/README.markdown b/README.markdown
--- a/README.markdown
+++ b/README.markdown
@@ -1,8 +1,6 @@
 linear
 ======
 
-[![Build Status](https://secure.travis-ci.org/ekmett/linear.png?branch=master)](http://travis-ci.org/ekmett/linear)
-
 Contact Information
 -------------------
 
diff --git a/linear.cabal b/linear.cabal
--- a/linear.cabal
+++ b/linear.cabal
@@ -1,6 +1,6 @@
 name:          linear
 category:      Math, Algebra
-version:       0.2.0.2
+version:       0.4.1
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
@@ -13,7 +13,7 @@
 synopsis:      Linear Algebra
 description:   Types and combinators for low-dimension-count linear algebra on free vector spaces
 build-type:    Simple
-tested-with:   GHC == 7.4.1, GHC == 7.6.1
+tested-with:   GHC == 7.4.2, GHC == 7.6.1
 extra-source-files:
   .travis.yml
   .ghci
@@ -29,11 +29,13 @@
 
 library
   build-depends:
-    base == 4.*,
-    distributive >= 0.2.2 && < 0.3,
-    lens >= 2.9 && < 3.1
+    base             >= 4.5 && < 5,
+    distributive     >= 0.2.2 && < 0.3,
+    lens             >= 3.6 && < 3.8,
+    template-haskell >= 2.7 && < 2.9
 
   exposed-modules:
+    Linear
     Linear.Conjugate
     Linear.Epsilon
     Linear.Matrix
@@ -53,10 +55,10 @@
   type:    exitcode-stdio-1.0
   main-is: doctests.hs
   build-depends:
-    base == 4.*,
+    base,
     directory >= 1.0 && < 1.2,
-    doctest >= 0.8 && < 0.10,
-    filepath >= 1.3 && < 1.4
+    doctest   >= 0.8 && < 0.10,
+    filepath  >= 1.3 && < 1.4
   ghc-options: -Wall -Werror -threaded
   hs-source-dirs: tests
 
diff --git a/src/Linear.hs b/src/Linear.hs
new file mode 100644
--- /dev/null
+++ b/src/Linear.hs
@@ -0,0 +1,13 @@
+-- |This module simply re-exports everything from the various modules
+-- that make up the linear package.
+module Linear (module X) where
+import Linear.Conjugate as X
+import Linear.Epsilon as X
+import Linear.Matrix as X
+import Linear.Metric as X
+import Linear.Plucker as X
+import Linear.Quaternion as X
+import Linear.V2 as X
+import Linear.V3 as X
+import Linear.V4 as X
+import Linear.Vector as X
diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -50,12 +50,15 @@
 type M44 a = V4 (V4 a)
 type M43 a = V4 (V3 a)
 
--- | Build a rotation matrix from a 'Quaternion'.
+-- | Build a rotation matrix from a unit 'Quaternion'.
 fromQuaternion :: Num a => Quaternion a -> M33 a
-fromQuaternion (Quaternion a (V3 b c d)) =
-  V3 (V3 (a*a+b*b-c*c-d*d) (2*b*c-2*a*d) (2*b*d+2*a*c))
-     (V3 (2*b*c+2*a*d) (a*a-b*b+c*c-d*d) (2*c*d-2*a*b))
-     (V3 (2*b*d-2*a*c) (2*c*d+2*a*b) (a*a-b*b-c*c+d*d))
+fromQuaternion (Quaternion w (V3 x y z)) =
+  V3 (V3 (1-2*(y2+z2)) (2*(x*y-z*w)) (2*(x*z+y*w)))
+     (V3 (2*(x*y+z*w)) (1-2*(x2+z2)) (2*(y*z-x*w)))
+     (V3 (2*(x*z-y*w)) (2*(y*z+x*w)) (1-2*(x2+y2)))
+  where x2 = x * x
+        y2 = y * y
+        z2 = z * z
 
 mkTransformationMat :: Num a => M33 a -> V3 a -> M44 a
 mkTransformationMat (V3 r1 r2 r3) (V3 tx ty tz) =
diff --git a/src/Linear/Quaternion.hs b/src/Linear/Quaternion.hs
--- a/src/Linear/Quaternion.hs
+++ b/src/Linear/Quaternion.hs
@@ -129,7 +129,7 @@
 
 instance Complicated Quaternion where
   _e f (Quaternion a v) = (\a' -> Quaternion a' v) <$> f a
-  _i f (Quaternion a v) = Quaternion a <$> traverseOf _x f v
+  _i f (Quaternion a v) = Quaternion a <$> _x f v
   --_i f (Quaternion a (V3 b c d)) = (\b' -> Quaternion a (V3 b' c d)) <$> f b
 
 class Complicated t => Hamiltonian t where
@@ -138,8 +138,8 @@
   _ijk :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)
 
 instance Hamiltonian Quaternion where
-  _j f (Quaternion a v) = Quaternion a <$> traverseOf _y f v
-  _k f (Quaternion a v) = Quaternion a <$> traverseOf _z f v
+  _j f (Quaternion a v) = Quaternion a <$> _y f v
+  _k f (Quaternion a v) = Quaternion a <$> _z f v
   -- _j f (Quaternion a (V3 b c d)) = (\c' -> Quaternion a (V3 b c' d)) <$> f c
   -- _k f (Quaternion a (V3 b c d)) = Quaternion a . V3 b c <$> f d
 
diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs
--- a/src/Linear/Vector.hs
+++ b/src/Linear/Vector.hs
@@ -17,9 +17,12 @@
   , (*^)
   , (^/)
   , lerp
+  , basis
+  , basisFor
   ) where
 
 import Control.Applicative
+import Control.Lens
 
 infixl 6 ^+^, ^-^
 infixl 7 ^*, *^, ^/
@@ -58,3 +61,17 @@
 lerp :: (Applicative f, Num a) => a -> f a -> f a -> f a
 lerp alpha u v = alpha *^ u ^+^ (1 - alpha) *^ v
 {-# INLINE lerp #-}
+
+-- | Produce a default basis for a vector space. If the dimensionality
+-- of the vector space is not statically known, see 'basisFor'.
+basis :: (Applicative t, Traversable t, Num a) => [t a]
+basis = [ set (element k) 1 zero | k <- [0..lengthOf folded zero - 1]]
+  where zero = pure 0
+
+-- | Produce a default basis for a vector space from which the
+-- argument is drawn.
+basisFor :: (Traversable t, Enum a, Num a) => t a -> [t a]
+basisFor v = map aux [0..n-1]
+  where z = 0 <$ v
+        n = lengthOf folded z
+        aux i = z & element i .~ 1