diff --git a/src/Data/Derivative.hs b/src/Data/Derivative.hs
--- a/src/Data/Derivative.hs
+++ b/src/Data/Derivative.hs
@@ -15,7 +15,8 @@
 
 module Data.Derivative
   (
-    (:>)(..), (:~>), dZero, dConst, dId, bilinearD
+    (:>)(..), (:~>), dZero, dConst, dId
+  , linearD, bilinearD
   , (@.), (>-<)
   ) where
 
@@ -85,12 +86,12 @@
 -- or
 --   dId v = D v dConst
 
--- Every linear function has a constant derivative equal to the function
+-- | Every linear function has a constant derivative equal to the function
 -- itself (as a linear map).
 linearD :: VectorSpace v s => (u :-* v) -> (u :~> v)
 linearD f u = D (f u) (dConst . f)
 
--- Derivative tower for applying a bilinear function, such as
+-- | Derivative tower for applying a bilinear function, such as
 -- multiplication.
 bilinearD :: VectorSpace w s =>
              (u -> v -> w) -> (t :> u) -> (t :> v) -> (t :> w)
@@ -116,7 +117,7 @@
     D c0 c' = h b0
 
 
--- Specialized chain rule.
+-- | Specialized chain rule.
 (>-<) :: VectorSpace b s => (b -> b) -> ((a :> b) -> (a :> s))
       -> (a :> b) -> (a :> b)
 f >-< f' = \ b@(D b0 b') -> D (f b0) ((f' b *^) . b')
diff --git a/src/Data/NumInstances.hs b/src/Data/NumInstances.hs
--- a/src/Data/NumInstances.hs
+++ b/src/Data/NumInstances.hs
@@ -70,6 +70,8 @@
 lift2 :: (a->u) -> (b->v) -> (a,b) -> (u,v)
 lift2 f g (a,b) = (f a, g b)
 
+-- Equivalently, lift2 = (***)
+
 instance (Num a, Num b) => Num (a,b) where
   fromInteger n   = (fromInteger n, fromInteger n)
   (a,b) + (a',b') = (a+a',b+b')
diff --git a/src/Data/VectorSpace.hs b/src/Data/VectorSpace.hs
--- a/src/Data/VectorSpace.hs
+++ b/src/Data/VectorSpace.hs
@@ -22,7 +22,7 @@
   ) where
 
 import Control.Applicative
-
+import Data.Complex hiding (magnitude)
 
 infixr 9 :-*
 infixr 7 *^, ^/, <.>
@@ -109,6 +109,20 @@
 
 instance InnerSpace Float Float where
   (<.>) = (*)
+
+instance (RealFloat v, VectorSpace v s) => VectorSpace (Complex v) s where
+  zeroV       = zeroV :+ zeroV
+  s*^(u :+ v) = s*^u :+ s*^v
+  (^+^)       = (+)
+  negateV     = negate
+
+instance (RealFloat v, InnerSpace v s, VectorSpace s s')
+     => InnerSpace (Complex v) s where
+  (u :+ v) <.> (u' :+ v') = (u <.> u') ^+^ (v <.> v')
+
+-- Hm.  The 'RealFloat' constraint is unfortunate here.  It's due to a
+-- questionable decision to place 'RealFloat' into the definition of the
+-- 'Complex' /type/, rather than in functions and instances as needed.
 
 -- With UndecidableInstances, I get
 --   Illegal instance declaration for `VectorSpace (u, v) s' (the
diff --git a/vector-space.cabal b/vector-space.cabal
--- a/vector-space.cabal
+++ b/vector-space.cabal
@@ -1,5 +1,5 @@
 Name:                vector-space
-Version:             0.1
+Version:             0.1.1
 Synopsis: 	     Vector & affine spaces, plus derivatives
 Category:            math
 Description: