diff --git a/Data/Vect/Double/Base.hs b/Data/Vect/Double/Base.hs
--- a/Data/Vect/Double/Base.hs
+++ b/Data/Vect/Double/Base.hs
@@ -137,7 +137,7 @@
   fromNormalRadius :: Flt -> u -> v
   fromNormalRadius t n = t *& fromNormal n 
 
--- | Projects the first vector onto the direction of the second (unit) vector
+-- | Projects the first vector down to the hyperplane orthogonal to the second (unit) vector
 project' :: (Vector v, UnitVector v u, DotProd v) => v -> u -> v
 project' what dir = projectUnsafe what (fromNormal dir)
 
@@ -603,6 +603,9 @@
       normsqr r1 + 
       normsqr r2
      
+instance Pointwise Mat2 where
+  pointwise (Mat2 x1 y1) (Mat2 x2 y2) = Mat2 (x1 &! x2) (y1 &! y2)
+       
 --------------------------------------------------------------------------------     
 -- Vec3 instances
 
@@ -785,6 +788,9 @@
       normsqr r1 + 
       normsqr r2 + 
       normsqr r3 
+
+instance Pointwise Mat3 where
+  pointwise (Mat3 x1 y1 z1) (Mat3 x2 y2 z2) = Mat3 (x1 &! x2) (y1 &! y2) (z1 &! z2)
     
 --------------------------------------------------------------------------------
 -- Vec4 instances
@@ -953,6 +959,9 @@
       normsqr r2 + 
       normsqr r3 + 
       normsqr r4  
+    
+instance Pointwise Mat4 where
+  pointwise (Mat4 x1 y1 z1 w1) (Mat4 x2 y2 z2 w2) = Mat4 (x1 &! x2) (y1 &! y2) (z1 &! z2) (w1 &! w2)
     
 --------------------------------------------------------------------------------
 -- Extend instances
diff --git a/Data/Vect/Double/Instances.hs b/Data/Vect/Double/Instances.hs
new file mode 100644
--- /dev/null
+++ b/Data/Vect/Double/Instances.hs
@@ -0,0 +1,167 @@
+{-# OPTIONS_GHC -DFlt=Double -DVECT_Double #-}
+
+-- | 'Eq', 'Num' and 'Fractional' instances for vectors and matrices.
+-- These make writing code much more convenient, but also much more 
+-- dangerous; thus you have to import this module explicitely.
+--
+-- In the case of Vector instances, all operations are pointwise
+-- (including multiplication and division), and scalars are implicitly
+-- converted to vectors so that all components of the resulting vectors
+-- are the equal to the given scalar. This gives a set of consistent
+-- instances.
+--
+-- In the case of Matrices, multiplication is usual matrix multiplication,
+-- division is not implemented, and scalars are converted to diagonal 
+-- matrices.
+--
+-- 'abs' and 'signum' are implemented to be 'normalize' and 'norm'
+-- (in the case of matrices, Frobenius norm).
+
+module Data.Vect.Flt.Instances where
+
+--------------------------------------------------------------------------------  
+  
+import Data.Vect.Flt.Base 
+
+--------------------------------------------------------------------------------  
+-- * Vectors
+
+instance Eq Vec2 where
+  Vec2 x y == Vec2 a b = (x==a && y==b)
+
+instance Num Vec2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec2 x x
+  abs = normalize
+  signum v = let x = norm v in Vec2 x x
+  
+instance Fractional Vec2 where
+  (Vec2 x y) / (Vec2 a b) = Vec2 (x/a) (y/b) 
+  fromRational a = let x = fromRational a in Vec2 x x 
+
+--------------------------------------------------------------------------------  
+
+instance Eq Vec3 where
+  Vec3 x y z == Vec3 a b c = (x==a && y==b && z==c)
+
+instance Num Vec3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec3 x x x
+  abs = normalize
+  signum v = let x = norm v in Vec3 x x x
+  
+instance Fractional Vec3 where
+  (Vec3 x y z) / (Vec3 a b c) = Vec3 (x/a) (y/b) (z/c)
+  fromRational a = let x = fromRational a in Vec3 x x x  
+  
+--------------------------------------------------------------------------------  
+
+instance Eq Vec4 where
+  Vec4 x y z w == Vec4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Vec4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec4 x x x x
+  abs = normalize
+  signum v = let x = norm v in Vec4 x x x x
+  
+instance Fractional Vec4 where
+  (Vec4 x y z w) / (Vec4 a b c d) = Vec4 (x/a) (y/b) (z/c) (w/d)
+  fromRational a = let x = fromRational a in Vec4 x x x x  
+
+--------------------------------------------------------------------------------  
+-- * Matrices  
+
+instance Eq Mat2 where
+  Mat2 x y == Mat2 a b = (x==a && y==b)
+
+instance Num Mat2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec2 x x) . frobeniusNorm
+  
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat2 x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat2 v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec2 x x
+    
+instance Fractional Mat2 where
+  -- (Mat2 x y) / (Mat2 a b) = Mat2 (x/a) (y/b) 
+  -- fromRational a = let x = fromRational a in Mat2 x x  
+  (/) = error "Mat2/division: not implemented"
+  fromRational = diag . fromRational
+  
+--------------------------------------------------------------------------------  
+    
+instance Eq Mat3 where
+  Mat3 x y z == Mat3 a b c = (x==a && y==b && z==c)
+
+instance Num Mat3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec3 x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat3 x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat3 v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec3 x x x
+    
+instance Fractional Mat3 where
+  -- (Mat3 x y z) / (Mat3 a b c) = Mat3 (x/a) (y/b) (z/c)
+  -- fromRational a = let x = fromRational a in Mat3 x x x  
+  (/) = error "Mat3/division: not implemented"
+  fromRational = diag . fromRational
+    
+--------------------------------------------------------------------------------  
+  
+instance Eq Mat4 where
+  Mat4 x y z w == Mat4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Mat4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec4 x x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat4 x x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat4 v v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec4 x x x x
+    
+instance Fractional Mat4 where
+  -- (Mat4 x y z w) / (Mat4 a b c d) = Mat4 (x/a) (y/b) (z/c) (w/d)
+  -- fromRational a = let x = fromRational a in Mat4 x x x x
+  (/) = error "Mat4/division: not implemented"
+  fromRational = diag . fromRational
+
+--------------------------------------------------------------------------------  
+    
diff --git a/Data/Vect/Double/OpenGL.hs b/Data/Vect/Double/OpenGL.hs
--- a/Data/Vect/Double/OpenGL.hs
+++ b/Data/Vect/Double/OpenGL.hs
@@ -144,7 +144,7 @@
   (Vec4 (2*n/(r-l)) 0 0 0)
   (Vec4 0 (2*n/(t-b)) 0 0)
   (Vec4 ((r+l)/(r-l)) ((t+b)/(t-b)) (-(f+n)/(f-n)) (-1))
-  (Vec4 0 0 (-2*f*n*(f-n)) 0)
+  (Vec4 0 0 (-2*f*n/(f-n)) 0)
   
 -- | The same as "frustumMatrix", but with a different parametrization.
 frustumMatrix2 {- ' CPP is sensitive to primes -}
@@ -152,6 +152,18 @@
   -> Vec3     -- ^ (right,bottom,far)
   -> Mat4 
 frustumMatrix2 (Vec3 l t n) (Vec3 r b f) = frustumMatrix (l,r) (b,t) (n,f)
+
+-- | Inverse of "frustumMatrix".
+inverseFrustumMatrix
+  :: (Flt,Flt)   -- ^ (left,right)
+  -> (Flt,Flt)   -- ^ (bottom,top)
+  -> (Flt,Flt)   -- ^ (near,far)
+  -> Mat4 
+inverseFrustumMatrix (l,r) (b,t) (n,f) = Mat4
+  (Vec4 (0.5*(r-l)/n) 0 0 0)
+  (Vec4 0 (0.5*(t-b)/n) 0 0)
+  (Vec4 0 0 0 (0.5*(n-f)/(f*n)))
+  (Vec4 (0.5*(r+l)/n) (0.5*(t+b)/n) (-1) (0.5*(f+n)/(f*n)))
 
 --------------------------------------------------------------------------------
 -- Vertex instances
diff --git a/Data/Vect/Float/Base.hs b/Data/Vect/Float/Base.hs
--- a/Data/Vect/Float/Base.hs
+++ b/Data/Vect/Float/Base.hs
@@ -137,7 +137,7 @@
   fromNormalRadius :: Flt -> u -> v
   fromNormalRadius t n = t *& fromNormal n 
 
--- | Projects the first vector onto the direction of the second (unit) vector
+-- | Projects the first vector down to the hyperplane orthogonal to the second (unit) vector
 project' :: (Vector v, UnitVector v u, DotProd v) => v -> u -> v
 project' what dir = projectUnsafe what (fromNormal dir)
 
@@ -603,6 +603,9 @@
       normsqr r1 + 
       normsqr r2
      
+instance Pointwise Mat2 where
+  pointwise (Mat2 x1 y1) (Mat2 x2 y2) = Mat2 (x1 &! x2) (y1 &! y2)
+       
 --------------------------------------------------------------------------------     
 -- Vec3 instances
 
@@ -785,6 +788,9 @@
       normsqr r1 + 
       normsqr r2 + 
       normsqr r3 
+
+instance Pointwise Mat3 where
+  pointwise (Mat3 x1 y1 z1) (Mat3 x2 y2 z2) = Mat3 (x1 &! x2) (y1 &! y2) (z1 &! z2)
     
 --------------------------------------------------------------------------------
 -- Vec4 instances
@@ -953,6 +959,9 @@
       normsqr r2 + 
       normsqr r3 + 
       normsqr r4  
+    
+instance Pointwise Mat4 where
+  pointwise (Mat4 x1 y1 z1 w1) (Mat4 x2 y2 z2 w2) = Mat4 (x1 &! x2) (y1 &! y2) (z1 &! z2) (w1 &! w2)
     
 --------------------------------------------------------------------------------
 -- Extend instances
diff --git a/Data/Vect/Float/Instances.hs b/Data/Vect/Float/Instances.hs
new file mode 100644
--- /dev/null
+++ b/Data/Vect/Float/Instances.hs
@@ -0,0 +1,167 @@
+{-# OPTIONS_GHC -DFlt=Float -DVECT_Float #-}
+
+-- | 'Eq', 'Num' and 'Fractional' instances for vectors and matrices.
+-- These make writing code much more convenient, but also much more 
+-- dangerous; thus you have to import this module explicitely.
+--
+-- In the case of Vector instances, all operations are pointwise
+-- (including multiplication and division), and scalars are implicitly
+-- converted to vectors so that all components of the resulting vectors
+-- are the equal to the given scalar. This gives a set of consistent
+-- instances.
+--
+-- In the case of Matrices, multiplication is usual matrix multiplication,
+-- division is not implemented, and scalars are converted to diagonal 
+-- matrices.
+--
+-- 'abs' and 'signum' are implemented to be 'normalize' and 'norm'
+-- (in the case of matrices, Frobenius norm).
+
+module Data.Vect.Flt.Instances where
+
+--------------------------------------------------------------------------------  
+  
+import Data.Vect.Flt.Base 
+
+--------------------------------------------------------------------------------  
+-- * Vectors
+
+instance Eq Vec2 where
+  Vec2 x y == Vec2 a b = (x==a && y==b)
+
+instance Num Vec2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec2 x x
+  abs = normalize
+  signum v = let x = norm v in Vec2 x x
+  
+instance Fractional Vec2 where
+  (Vec2 x y) / (Vec2 a b) = Vec2 (x/a) (y/b) 
+  fromRational a = let x = fromRational a in Vec2 x x 
+
+--------------------------------------------------------------------------------  
+
+instance Eq Vec3 where
+  Vec3 x y z == Vec3 a b c = (x==a && y==b && z==c)
+
+instance Num Vec3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec3 x x x
+  abs = normalize
+  signum v = let x = norm v in Vec3 x x x
+  
+instance Fractional Vec3 where
+  (Vec3 x y z) / (Vec3 a b c) = Vec3 (x/a) (y/b) (z/c)
+  fromRational a = let x = fromRational a in Vec3 x x x  
+  
+--------------------------------------------------------------------------------  
+
+instance Eq Vec4 where
+  Vec4 x y z w == Vec4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Vec4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec4 x x x x
+  abs = normalize
+  signum v = let x = norm v in Vec4 x x x x
+  
+instance Fractional Vec4 where
+  (Vec4 x y z w) / (Vec4 a b c d) = Vec4 (x/a) (y/b) (z/c) (w/d)
+  fromRational a = let x = fromRational a in Vec4 x x x x  
+
+--------------------------------------------------------------------------------  
+-- * Matrices  
+
+instance Eq Mat2 where
+  Mat2 x y == Mat2 a b = (x==a && y==b)
+
+instance Num Mat2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec2 x x) . frobeniusNorm
+  
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat2 x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat2 v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec2 x x
+    
+instance Fractional Mat2 where
+  -- (Mat2 x y) / (Mat2 a b) = Mat2 (x/a) (y/b) 
+  -- fromRational a = let x = fromRational a in Mat2 x x  
+  (/) = error "Mat2/division: not implemented"
+  fromRational = diag . fromRational
+  
+--------------------------------------------------------------------------------  
+    
+instance Eq Mat3 where
+  Mat3 x y z == Mat3 a b c = (x==a && y==b && z==c)
+
+instance Num Mat3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec3 x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat3 x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat3 v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec3 x x x
+    
+instance Fractional Mat3 where
+  -- (Mat3 x y z) / (Mat3 a b c) = Mat3 (x/a) (y/b) (z/c)
+  -- fromRational a = let x = fromRational a in Mat3 x x x  
+  (/) = error "Mat3/division: not implemented"
+  fromRational = diag . fromRational
+    
+--------------------------------------------------------------------------------  
+  
+instance Eq Mat4 where
+  Mat4 x y z w == Mat4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Mat4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec4 x x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat4 x x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat4 v v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec4 x x x x
+    
+instance Fractional Mat4 where
+  -- (Mat4 x y z w) / (Mat4 a b c d) = Mat4 (x/a) (y/b) (z/c) (w/d)
+  -- fromRational a = let x = fromRational a in Mat4 x x x x
+  (/) = error "Mat4/division: not implemented"
+  fromRational = diag . fromRational
+
+--------------------------------------------------------------------------------  
+    
diff --git a/Data/Vect/Float/OpenGL.hs b/Data/Vect/Float/OpenGL.hs
--- a/Data/Vect/Float/OpenGL.hs
+++ b/Data/Vect/Float/OpenGL.hs
@@ -144,7 +144,7 @@
   (Vec4 (2*n/(r-l)) 0 0 0)
   (Vec4 0 (2*n/(t-b)) 0 0)
   (Vec4 ((r+l)/(r-l)) ((t+b)/(t-b)) (-(f+n)/(f-n)) (-1))
-  (Vec4 0 0 (-2*f*n*(f-n)) 0)
+  (Vec4 0 0 (-2*f*n/(f-n)) 0)
   
 -- | The same as "frustumMatrix", but with a different parametrization.
 frustumMatrix2 {- ' CPP is sensitive to primes -}
@@ -152,6 +152,18 @@
   -> Vec3     -- ^ (right,bottom,far)
   -> Mat4 
 frustumMatrix2 (Vec3 l t n) (Vec3 r b f) = frustumMatrix (l,r) (b,t) (n,f)
+
+-- | Inverse of "frustumMatrix".
+inverseFrustumMatrix
+  :: (Flt,Flt)   -- ^ (left,right)
+  -> (Flt,Flt)   -- ^ (bottom,top)
+  -> (Flt,Flt)   -- ^ (near,far)
+  -> Mat4 
+inverseFrustumMatrix (l,r) (b,t) (n,f) = Mat4
+  (Vec4 (0.5*(r-l)/n) 0 0 0)
+  (Vec4 0 (0.5*(t-b)/n) 0 0)
+  (Vec4 0 0 0 (0.5*(n-f)/(f*n)))
+  (Vec4 (0.5*(r+l)/n) (0.5*(t+b)/n) (-1) (0.5*(f+n)/(f*n)))
 
 --------------------------------------------------------------------------------
 -- Vertex instances
diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright (c) 2008-2009, Balazs Komuves
+Copyright (c) 2008-2010, Balazs Komuves
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without
diff --git a/src/flt/Base.hs b/src/flt/Base.hs
--- a/src/flt/Base.hs
+++ b/src/flt/Base.hs
@@ -136,7 +136,7 @@
   fromNormalRadius :: Flt -> u -> v
   fromNormalRadius t n = t *& fromNormal n 
 
--- | Projects the first vector onto the direction of the second (unit) vector
+-- | Projects the first vector down to the hyperplane orthogonal to the second (unit) vector
 project' :: (Vector v, UnitVector v u, DotProd v) => v -> u -> v
 project' what dir = projectUnsafe what (fromNormal dir)
 
@@ -602,6 +602,9 @@
       normsqr r1 + 
       normsqr r2
      
+instance Pointwise Mat2 where
+  pointwise (Mat2 x1 y1) (Mat2 x2 y2) = Mat2 (x1 &! x2) (y1 &! y2)
+       
 --------------------------------------------------------------------------------     
 -- Vec3 instances
 
@@ -784,6 +787,9 @@
       normsqr r1 + 
       normsqr r2 + 
       normsqr r3 
+
+instance Pointwise Mat3 where
+  pointwise (Mat3 x1 y1 z1) (Mat3 x2 y2 z2) = Mat3 (x1 &! x2) (y1 &! y2) (z1 &! z2)
     
 --------------------------------------------------------------------------------
 -- Vec4 instances
@@ -952,6 +958,9 @@
       normsqr r2 + 
       normsqr r3 + 
       normsqr r4  
+    
+instance Pointwise Mat4 where
+  pointwise (Mat4 x1 y1 z1 w1) (Mat4 x2 y2 z2 w2) = Mat4 (x1 &! x2) (y1 &! y2) (z1 &! z2) (w1 &! w2)
     
 --------------------------------------------------------------------------------
 -- Extend instances
diff --git a/src/flt/Instances.hs b/src/flt/Instances.hs
new file mode 100644
--- /dev/null
+++ b/src/flt/Instances.hs
@@ -0,0 +1,166 @@
+
+-- | 'Eq', 'Num' and 'Fractional' instances for vectors and matrices.
+-- These make writing code much more convenient, but also much more 
+-- dangerous; thus you have to import this module explicitely.
+--
+-- In the case of Vector instances, all operations are pointwise
+-- (including multiplication and division), and scalars are implicitly
+-- converted to vectors so that all components of the resulting vectors
+-- are the equal to the given scalar. This gives a set of consistent
+-- instances.
+--
+-- In the case of Matrices, multiplication is usual matrix multiplication,
+-- division is not implemented, and scalars are converted to diagonal 
+-- matrices.
+--
+-- 'abs' and 'signum' are implemented to be 'normalize' and 'norm'
+-- (in the case of matrices, Frobenius norm).
+
+module Data.Vect.Flt.Instances where
+
+--------------------------------------------------------------------------------  
+  
+import Data.Vect.Flt.Base 
+
+--------------------------------------------------------------------------------  
+-- * Vectors
+
+instance Eq Vec2 where
+  Vec2 x y == Vec2 a b = (x==a && y==b)
+
+instance Num Vec2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec2 x x
+  abs = normalize
+  signum v = let x = norm v in Vec2 x x
+  
+instance Fractional Vec2 where
+  (Vec2 x y) / (Vec2 a b) = Vec2 (x/a) (y/b) 
+  fromRational a = let x = fromRational a in Vec2 x x 
+
+--------------------------------------------------------------------------------  
+
+instance Eq Vec3 where
+  Vec3 x y z == Vec3 a b c = (x==a && y==b && z==c)
+
+instance Num Vec3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec3 x x x
+  abs = normalize
+  signum v = let x = norm v in Vec3 x x x
+  
+instance Fractional Vec3 where
+  (Vec3 x y z) / (Vec3 a b c) = Vec3 (x/a) (y/b) (z/c)
+  fromRational a = let x = fromRational a in Vec3 x x x  
+  
+--------------------------------------------------------------------------------  
+
+instance Eq Vec4 where
+  Vec4 x y z w == Vec4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Vec4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  (*) = pointwise 
+  fromInteger a = let x = fromInteger a in Vec4 x x x x
+  abs = normalize
+  signum v = let x = norm v in Vec4 x x x x
+  
+instance Fractional Vec4 where
+  (Vec4 x y z w) / (Vec4 a b c d) = Vec4 (x/a) (y/b) (z/c) (w/d)
+  fromRational a = let x = fromRational a in Vec4 x x x x  
+
+--------------------------------------------------------------------------------  
+-- * Matrices  
+
+instance Eq Mat2 where
+  Mat2 x y == Mat2 a b = (x==a && y==b)
+
+instance Num Mat2 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+  
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec2 x x) . frobeniusNorm
+  
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat2 x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat2 v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec2 x x
+    
+instance Fractional Mat2 where
+  -- (Mat2 x y) / (Mat2 a b) = Mat2 (x/a) (y/b) 
+  -- fromRational a = let x = fromRational a in Mat2 x x  
+  (/) = error "Mat2/division: not implemented"
+  fromRational = diag . fromRational
+  
+--------------------------------------------------------------------------------  
+    
+instance Eq Mat3 where
+  Mat3 x y z == Mat3 a b c = (x==a && y==b && z==c)
+
+instance Num Mat3 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec3 x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat3 x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat3 v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec3 x x x
+    
+instance Fractional Mat3 where
+  -- (Mat3 x y z) / (Mat3 a b c) = Mat3 (x/a) (y/b) (z/c)
+  -- fromRational a = let x = fromRational a in Mat3 x x x  
+  (/) = error "Mat3/division: not implemented"
+  fromRational = diag . fromRational
+    
+--------------------------------------------------------------------------------  
+  
+instance Eq Mat4 where
+  Mat4 x y z w == Mat4 a b c d = (x==a && y==b && z==c && w==d)
+
+instance Num Mat4 where
+  (+) = (&+)
+  (-) = (&-)
+  negate = neg
+
+  (*) = (.*.)
+  fromInteger = diag . fromInteger
+  abs m = m &* (1.0 / frobeniusNorm m)
+  signum = diag . (\x -> Vec4 x x x x) . frobeniusNorm
+
+  -- (*) = pointwise 
+  -- fromInteger a = let x = fromInteger a in Mat4 x x x x
+  -- abs m = m &* (1.0 / frobeniusNorm m)
+  -- signum m = Mat4 v v v v where
+  --   x = frobeniusNorm m 
+  --   v = Vec4 x x x x
+    
+instance Fractional Mat4 where
+  -- (Mat4 x y z w) / (Mat4 a b c d) = Mat4 (x/a) (y/b) (z/c) (w/d)
+  -- fromRational a = let x = fromRational a in Mat4 x x x x
+  (/) = error "Mat4/division: not implemented"
+  fromRational = diag . fromRational
+
+--------------------------------------------------------------------------------  
+    
diff --git a/src/flt/OpenGL.hs b/src/flt/OpenGL.hs
--- a/src/flt/OpenGL.hs
+++ b/src/flt/OpenGL.hs
@@ -143,7 +143,7 @@
   (Vec4 (2*n/(r-l)) 0 0 0)
   (Vec4 0 (2*n/(t-b)) 0 0)
   (Vec4 ((r+l)/(r-l)) ((t+b)/(t-b)) (-(f+n)/(f-n)) (-1))
-  (Vec4 0 0 (-2*f*n*(f-n)) 0)
+  (Vec4 0 0 (-2*f*n/(f-n)) 0)
   
 -- | The same as "frustumMatrix", but with a different parametrization.
 frustumMatrix2 {- ' CPP is sensitive to primes -}
@@ -151,6 +151,18 @@
   -> Vec3     -- ^ (right,bottom,far)
   -> Mat4 
 frustumMatrix2 (Vec3 l t n) (Vec3 r b f) = frustumMatrix (l,r) (b,t) (n,f)
+
+-- | Inverse of "frustumMatrix".
+inverseFrustumMatrix
+  :: (Flt,Flt)   -- ^ (left,right)
+  -> (Flt,Flt)   -- ^ (bottom,top)
+  -> (Flt,Flt)   -- ^ (near,far)
+  -> Mat4 
+inverseFrustumMatrix (l,r) (b,t) (n,f) = Mat4
+  (Vec4 (0.5*(r-l)/n) 0 0 0)
+  (Vec4 0 (0.5*(t-b)/n) 0 0)
+  (Vec4 0 0 0 (0.5*(n-f)/(f*n)))
+  (Vec4 (0.5*(r+l)/n) (0.5*(t+b)/n) (-1) (0.5*(f+n)/(f*n)))
 
 --------------------------------------------------------------------------------
 -- Vertex instances
diff --git a/vect.cabal b/vect.cabal
--- a/vect.cabal
+++ b/vect.cabal
@@ -1,5 +1,5 @@
 Name:                vect
-Version:             0.4.5
+Version:             0.4.5.2
 Synopsis:            A low-dimensional linear algebra library, tailored to computer graphics.
 Description:         A low-dimensional (2, 3 and 4) linear algebra library, 
                      with lots of useful functions. Intended usage is primarily 
@@ -10,7 +10,7 @@
 License:             BSD3
 License-file:        LICENSE
 Author:              Balazs Komuves
-Copyright:           (c) 2008-2009 Balazs Komuves
+Copyright:           (c) 2008-2010 Balazs Komuves
 Maintainer:          bkomuves (plus) hackage (at) gmail (dot) com
 Homepage:            http://code.haskell.org/~bkomuves/
 Stability:           Experimental
@@ -27,7 +27,8 @@
                      src/flt/Util/Dim2.hs,
                      src/flt/Util/Dim3.hs,
                      src/flt/Util/Dim4.hs,
-                     src/flt/Util/Projective.hs
+                     src/flt/Util/Projective.hs,
+                     src/flt/Instances.hs
                      
 Flag splitBase
   Description: Choose the new smaller, split-up base package.
@@ -38,9 +39,10 @@
   
 Library
   if flag(splitBase)
-    Build-Depends:       base >= 3, random 
+    Build-Depends:       base >= 3 && < 5
+    Build-Depends:       random 
   else
-    Build-Depends:       base <  3
+    Build-Depends:       base >= 2 && < 3
 
   if flag(OpenGL)
     Build-Depends:       OpenGL
@@ -58,6 +60,7 @@
                        Data.Vect.Float.Util.Dim3, 
                        Data.Vect.Float.Util.Dim4,
                        Data.Vect.Float.Util.Projective,
+                       Data.Vect.Float.Instances
 
                        Data.Vect.Double,
                        Data.Vect.Double.Base, 
@@ -66,7 +69,8 @@
                        Data.Vect.Double.Util.Dim2, 
                        Data.Vect.Double.Util.Dim3, 
                        Data.Vect.Double.Util.Dim4,
-                       Data.Vect.Double.Util.Projective
+                       Data.Vect.Double.Util.Projective,
+                       Data.Vect.Double.Instances
 
   Hs-Source-Dirs:      .
   Extensions:          ForeignFunctionInterface, CPP,