diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,12 @@
+1.12.1
+------
+* Added "swizzle" lenses **e.g.** `_yzx`, which are useful for working with libraries like `gl`.
+
+1.12
+------
+* Added 'transpose'
+* Added missing 'Mxy' matrices up to 4 dimensions -- they were commonly reimplemented by users.
+
 1.11.3
 ------
 * Fixed an issue with `UndecidableInstances` on GHC 7.6.3
diff --git a/linear.cabal b/linear.cabal
--- a/linear.cabal
+++ b/linear.cabal
@@ -1,6 +1,6 @@
 name:          linear
 category:      Math, Algebra
-version:       1.11.3
+version:       1.12.1
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -18,11 +18,13 @@
   ( (!*!), (!+!), (!-!), (!*) , (*!), (!!*), (*!!)
   , column
   , adjoint
-  , M22, M33, M44, M43, m33_to_m44, m43_to_m44
+  , M22, M23, M24, M32, M33, M34, M42, M43, M44
+  , m33_to_m44, m43_to_m44
   , det22, det33, inv22, inv33
   , eye2, eye3, eye4
   , Trace(..)
   , translation
+  , transpose
   , fromQuaternion
   , mkTransformation
   , mkTransformationMat
@@ -146,12 +148,22 @@
 
 -- | A 2x2 matrix with row-major representation
 type M22 a = V2 (V2 a)
+-- | A 2x3 matrix with row-major representation
+type M23 a = V2 (V3 a)
+-- | A 2x3 matrix with row-major representation
+type M24 a = V2 (V4 a)
+-- | A 3x2 matrix with row-major representation
+type M32 a = V3 (V2 a)
 -- | A 3x3 matrix with row-major representation
 type M33 a = V3 (V3 a)
--- | A 4x4 matrix with row-major representation
-type M44 a = V4 (V4 a)
+-- | A 3x4 matrix with row-major representation
+type M34 a = V3 (V4 a)
+-- | A 4x2 matrix with row-major representation
+type M42 a = V4 (V2 a)
 -- | A 4x3 matrix with row-major representation
 type M43 a = V4 (V3 a)
+-- | A 4x4 matrix with row-major representation
+type M44 a = V4 (V4 a)
 
 -- | Build a rotation matrix from a unit 'Quaternion'.
 fromQuaternion :: Num a => Quaternion a -> M33 a
@@ -287,3 +299,10 @@
         det = det33 m
 {-# INLINE inv33 #-}
 
+
+-- | 'transpose' is just an alias for 'distribute'
+--
+-- > transpose (V3 (V2 1 2) (V2 3 4) (V2 5 6))
+-- V2 (V3 1 3 5) (V3 2 4 6)
+transpose :: (Distributive g, Functor f) => f (g a) -> g (f a)
+transpose = distribute
diff --git a/src/Linear/Perspective.hs b/src/Linear/Perspective.hs
--- a/src/Linear/Perspective.hs
+++ b/src/Linear/Perspective.hs
@@ -73,7 +73,7 @@
      (V4 0 y 0    0)
      (V4 0 0 (-1) w)
      (V4 0 0 (-1) 0)
-  where range  = (tan (fovy / 2)) * near
+  where range  = tan (fovy / 2) * near
         left   = -range * aspect
         right  = range * aspect
         bottom = -range
diff --git a/src/Linear/V2.hs b/src/Linear/V2.hs
--- a/src/Linear/V2.hs
+++ b/src/Linear/V2.hs
@@ -2,6 +2,7 @@
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 -- {-# OPTIONS_GHC -fno-warn-name-shadowing #-}
 {-# LANGUAGE CPP #-}
@@ -24,6 +25,7 @@
   ( V2(..)
   , R1(..)
   , R2(..)
+  , _yx
   , ex, ey
   , perp
   , angle
@@ -182,18 +184,18 @@
   -- >>> V2 1 2 & _y .~ 3
   -- V2 1 3
   --
-  -- @
-  -- '_y' :: 'Lens'' (t a) a
-  -- @
-  _y :: Functor f => (a -> f a) -> t a -> f (t a)
+  _y :: Lens' (t a) a
   _y = _xy._y
   {-# INLINE _y #-}
 
-  -- |
-  -- @
-  -- '_xy' :: 'Lens'' (t a) ('V2' a)
-  -- @
-  _xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a)
+  _xy :: Lens' (t a) (V2 a)
+
+-- |
+-- >>> V2 1 2 ^. _yx
+-- V2 2 1
+_yx :: R2 t => Lens' (t a) (V2 a)
+_yx f = _xy $ \(V2 a b) -> f (V2 b a) <&> \(V2 b' a') -> V2 a' b'
+{-# INLINE _yx #-}
 
 ey :: R2 t => E t
 ey = E _y
diff --git a/src/Linear/V3.hs b/src/Linear/V3.hs
--- a/src/Linear/V3.hs
+++ b/src/Linear/V3.hs
@@ -2,6 +2,7 @@
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE CPP #-}
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
@@ -24,7 +25,10 @@
   , cross, triple
   , R1(..)
   , R2(..)
+  , _yx
   , R3(..)
+  , _xz, _yz, _zx, _zy
+  , _xzy, _yxz, _yzx, _zxy, _zyx
   , ex, ey, ez
   ) where
 
@@ -166,15 +170,42 @@
 -- | A space that distinguishes 3 orthogonal basis vectors: '_x', '_y', and '_z'. (It may have more)
 class R2 t => R3 t where
   -- |
-  -- @
-  -- '_z' :: 'Lens'' (t a) a
-  -- @
-  _z :: Functor f => (a -> f a) -> t a -> f (t a)
-  -- |
-  -- @
-  -- '_xyz' :: 'Lens'' (t a) ('V3' a)
-  -- @
-  _xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)
+  -- >>> V3 1 2 3 ^. _z
+  -- 3
+  _z :: Lens' (t a) a
+
+  _xyz :: Lens' (t a) (V3 a)
+
+_xz, _yz, _zx, _zy :: R3 t => Lens' (t a) (V2 a)
+
+_xz f = _xyz $ \(V3 a b c) -> f (V2 a c) <&> \(V2 a' c') -> V3 a' b c'
+{-# INLINE _xz #-}
+
+_yz f = _xyz $ \(V3 a b c) -> f (V2 b c) <&> \(V2 b' c') -> V3 a b' c'
+{-# INLINE _yz #-}
+
+_zx f = _xyz $ \(V3 a b c) -> f (V2 c a) <&> \(V2 c' a') -> V3 a' b c'
+{-# INLINE _zx #-}
+
+_zy f = _xyz $ \(V3 a b c) -> f (V2 c b) <&> \(V2 c' b') -> V3 a b' c'
+{-# INLINE _zy #-}
+
+_xzy, _yxz, _yzx, _zxy, _zyx :: R3 t => Lens' (t a) (V3 a)
+
+_xzy f = _xyz $ \(V3 a b c) -> f (V3 a c b) <&> \(V3 a' c' b') -> V3 a' b' c'
+{-# INLINE _xzy #-}
+
+_yxz f = _xyz $ \(V3 a b c) -> f (V3 b a c) <&> \(V3 b' a' c') -> V3 a' b' c'
+{-# INLINE _yxz #-}
+
+_yzx f = _xyz $ \(V3 a b c) -> f (V3 b c a) <&> \(V3 b' c' a') -> V3 a' b' c'
+{-# INLINE _yzx #-}
+
+_zxy f = _xyz $ \(V3 a b c) -> f (V3 c a b) <&> \(V3 c' a' b') -> V3 a' b' c'
+{-# INLINE _zxy #-}
+
+_zyx f = _xyz $ \(V3 a b c) -> f (V3 c b a) <&> \(V3 c' b' a') -> V3 a' b' c'
+{-# INLINE _zyx #-}
 
 ez :: R3 t => E t
 ez = E _z
diff --git a/src/Linear/V4.hs b/src/Linear/V4.hs
--- a/src/Linear/V4.hs
+++ b/src/Linear/V4.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE DeriveDataTypeable #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE CPP #-}
@@ -24,8 +25,17 @@
   , vector, point, normalizePoint
   , R1(..)
   , R2(..)
+  , _yx
   , R3(..)
+  , _xz, _yz, _zx, _zy
+  , _xzy, _yxz, _yzx, _zxy, _zyx
   , R4(..)
+  , _xw, _yw, _zw, _wx, _wy, _wz
+  , _xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy
+  , _wxy, _wxz, _wyx, _wyz, _wzx, _wzy
+  , _xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz
+  , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz
+  , _wyzx, _wzxy, _wzyx
   , ex, ey, ez, ew
   ) where
 
@@ -172,15 +182,156 @@
 -- | A space that distinguishes orthogonal basis vectors '_x', '_y', '_z', '_w'. (It may have more.)
 class R3 t => R4 t where
   -- |
-  -- @
-  -- '_w' :: 'Lens'' (t a) a
-  -- @
-  _w :: Functor f => (a -> f a) -> t a -> f (t a)
-  -- |
-  -- @
-  -- '_xyzw' :: 'Lens'' (t a) ('V4' a)
-  -- @
-  _xyzw :: Functor f => (V4 a -> f (V4 a)) -> t a -> f (t a)
+  -- >>> V4 1 2 3 4 ^._w
+  -- 4
+  _w :: Lens' (t a) a
+  _xyzw :: Lens' (t a) (V4 a)
+
+_xw, _yw, _zw, _wx, _wy, _wz :: R4 t => Lens' (t a) (V2 a)
+_xw f = _xyzw $ \(V4 a b c d) -> f (V2 a d) <&> \(V2 a' d') -> V4 a' b c d'
+{-# INLINE _xw #-}
+
+_yw f = _xyzw $ \(V4 a b c d) -> f (V2 b d) <&> \(V2 b' d') -> V4 a b' c d'
+{-# INLINE _yw #-}
+
+_zw f = _xyzw $ \(V4 a b c d) -> f (V2 c d) <&> \(V2 c' d') -> V4 a b c' d'
+{-# INLINE _zw #-}
+
+_wx f = _xyzw $ \(V4 a b c d) -> f (V2 d a) <&> \(V2 d' a') -> V4 a' b c d'
+{-# INLINE _wx #-}
+
+_wy f = _xyzw $ \(V4 a b c d) -> f (V2 d b) <&> \(V2 d' b') -> V4 a b' c d'
+{-# INLINE _wy #-}
+
+_wz f = _xyzw $ \(V4 a b c d) -> f (V2 d c) <&> \(V2 d' c') -> V4 a b c' d'
+{-# INLINE _wz #-}
+
+_xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy, _wxy, _wxz, _wyx, _wyz, _wzx, _wzy :: R4 t => Lens' (t a) (V3 a)
+_xyw f = _xyzw $ \(V4 a b c d) -> f (V3 a b d) <&> \(V3 a' b' d') -> V4 a' b' c d'
+{-# INLINE _xyw #-}
+
+_xzw f = _xyzw $ \(V4 a b c d) -> f (V3 a c d) <&> \(V3 a' c' d') -> V4 a' b c' d'
+{-# INLINE _xzw #-}
+
+_xwy f = _xyzw $ \(V4 a b c d) -> f (V3 a d b) <&> \(V3 a' d' b') -> V4 a' b' c d'
+{-# INLINE _xwy #-}
+
+_xwz f = _xyzw $ \(V4 a b c d) -> f (V3 a d c) <&> \(V3 a' d' c') -> V4 a' b c' d'
+{-# INLINE _xwz #-}
+
+_yxw f = _xyzw $ \(V4 a b c d) -> f (V3 b a d) <&> \(V3 b' a' d') -> V4 a' b' c d'
+{-# INLINE _yxw #-}
+
+_yzw f = _xyzw $ \(V4 a b c d) -> f (V3 b c d) <&> \(V3 b' c' d') -> V4 a b' c' d'
+{-# INLINE _yzw #-}
+
+_ywx f = _xyzw $ \(V4 a b c d) -> f (V3 b d a) <&> \(V3 b' d' a') -> V4 a' b' c d'
+{-# INLINE _ywx #-}
+
+_ywz f = _xyzw $ \(V4 a b c d) -> f (V3 b d c) <&> \(V3 b' d' c') -> V4 a b' c' d'
+{-# INLINE _ywz #-}
+
+_zxw f = _xyzw $ \(V4 a b c d) -> f (V3 c a d) <&> \(V3 c' a' d') -> V4 a' b c' d'
+{-# INLINE _zxw #-}
+
+_zyw f = _xyzw $ \(V4 a b c d) -> f (V3 c b d) <&> \(V3 c' b' d') -> V4 a b' c' d'
+{-# INLINE _zyw #-}
+
+_zwx f = _xyzw $ \(V4 a b c d) -> f (V3 c d a) <&> \(V3 c' d' a') -> V4 a' b c' d'
+{-# INLINE _zwx #-}
+
+_zwy f = _xyzw $ \(V4 a b c d) -> f (V3 c d b) <&> \(V3 c' d' b') -> V4 a b' c' d'
+{-# INLINE _zwy #-}
+
+_wxy f = _xyzw $ \(V4 a b c d) -> f (V3 d a b) <&> \(V3 d' a' b') -> V4 a' b' c d'
+{-# INLINE _wxy #-}
+
+_wxz f = _xyzw $ \(V4 a b c d) -> f (V3 d a c) <&> \(V3 d' a' c') -> V4 a' b c' d'
+{-# INLINE _wxz #-}
+
+_wyx f = _xyzw $ \(V4 a b c d) -> f (V3 d b a) <&> \(V3 d' b' a') -> V4 a' b' c d'
+{-# INLINE _wyx #-}
+
+_wyz f = _xyzw $ \(V4 a b c d) -> f (V3 d b c) <&> \(V3 d' b' c') -> V4 a b' c' d'
+{-# INLINE _wyz #-}
+
+_wzx f = _xyzw $ \(V4 a b c d) -> f (V3 d c a) <&> \(V3 d' c' a') -> V4 a' b c' d'
+{-# INLINE _wzx #-}
+
+_wzy f = _xyzw $ \(V4 a b c d) -> f (V3 d c b) <&> \(V3 d' c' b') -> V4 a b' c' d'
+{-# INLINE _wzy #-}
+
+_xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz
+  , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz
+  , _wyzx, _wzxy, _wzyx :: R4 t => Lens' (t a) (V4 a)
+_xywz f = _xyzw $ \(V4 a b c d) -> f (V4 a b d c) <&> \(V4 a' b' d' c') -> V4 a' b' c' d'
+{-# INLINE _xywz #-}
+
+_xzyw f = _xyzw $ \(V4 a b c d) -> f (V4 a c b d) <&> \(V4 a' c' b' d') -> V4 a' b' c' d'
+{-# INLINE _xzyw #-}
+
+_xzwy f = _xyzw $ \(V4 a b c d) -> f (V4 a c d b) <&> \(V4 a' c' d' b') -> V4 a' b' c' d'
+{-# INLINE _xzwy #-}
+
+_xwyz f = _xyzw $ \(V4 a b c d) -> f (V4 a d b c) <&> \(V4 a' d' b' c') -> V4 a' b' c' d'
+{-# INLINE _xwyz #-}
+
+_xwzy f = _xyzw $ \(V4 a b c d) -> f (V4 a d c b) <&> \(V4 a' d' c' b') -> V4 a' b' c' d'
+{-# INLINE _xwzy #-}
+
+_yxzw f = _xyzw $ \(V4 a b c d) -> f (V4 b a c d) <&> \(V4 b' a' c' d') -> V4 a' b' c' d'
+{-# INLINE _yxzw #-}
+
+_yxwz f = _xyzw $ \(V4 a b c d) -> f (V4 b a d c) <&> \(V4 b' a' d' c') -> V4 a' b' c' d'
+{-# INLINE _yxwz #-}
+
+_yzxw f = _xyzw $ \(V4 a b c d) -> f (V4 b c a d) <&> \(V4 b' c' a' d') -> V4 a' b' c' d'
+{-# INLINE _yzxw #-}
+
+_yzwx f = _xyzw $ \(V4 a b c d) -> f (V4 b c d a) <&> \(V4 b' c' d' a') -> V4 a' b' c' d'
+{-# INLINE _yzwx #-}
+
+_ywxz f = _xyzw $ \(V4 a b c d) -> f (V4 b d a c) <&> \(V4 b' d' a' c') -> V4 a' b' c' d'
+{-# INLINE _ywxz #-}
+
+_ywzx f = _xyzw $ \(V4 a b c d) -> f (V4 b d c a) <&> \(V4 b' d' c' a') -> V4 a' b' c' d'
+{-# INLINE _ywzx #-}
+
+_zxyw f = _xyzw $ \(V4 a b c d) -> f (V4 c a b d) <&> \(V4 c' a' b' d') -> V4 a' b' c' d'
+{-# INLINE _zxyw #-}
+
+_zxwy f = _xyzw $ \(V4 a b c d) -> f (V4 c a d b) <&> \(V4 c' a' d' b') -> V4 a' b' c' d'
+{-# INLINE _zxwy #-}
+
+_zyxw f = _xyzw $ \(V4 a b c d) -> f (V4 c b a d) <&> \(V4 c' b' a' d') -> V4 a' b' c' d'
+{-# INLINE _zyxw #-}
+
+_zywx f = _xyzw $ \(V4 a b c d) -> f (V4 c b d a) <&> \(V4 c' b' d' a') -> V4 a' b' c' d'
+{-# INLINE _zywx #-}
+
+_zwxy f = _xyzw $ \(V4 a b c d) -> f (V4 c d a b) <&> \(V4 c' d' a' b') -> V4 a' b' c' d'
+{-# INLINE _zwxy #-}
+
+_zwyx f = _xyzw $ \(V4 a b c d) -> f (V4 c d b a) <&> \(V4 c' d' b' a') -> V4 a' b' c' d'
+{-# INLINE _zwyx #-}
+
+_wxyz f = _xyzw $ \(V4 a b c d) -> f (V4 d a b c) <&> \(V4 d' a' b' c') -> V4 a' b' c' d'
+{-# INLINE _wxyz #-}
+
+_wxzy f = _xyzw $ \(V4 a b c d) -> f (V4 d a c b) <&> \(V4 d' a' c' b') -> V4 a' b' c' d'
+{-# INLINE _wxzy #-}
+
+_wyxz f = _xyzw $ \(V4 a b c d) -> f (V4 d b a c) <&> \(V4 d' b' a' c') -> V4 a' b' c' d'
+{-# INLINE _wyxz #-}
+
+_wyzx f = _xyzw $ \(V4 a b c d) -> f (V4 d b c a) <&> \(V4 d' b' c' a') -> V4 a' b' c' d'
+{-# INLINE _wyzx #-}
+
+_wzxy f = _xyzw $ \(V4 a b c d) -> f (V4 d c a b) <&> \(V4 d' c' a' b') -> V4 a' b' c' d'
+{-# INLINE _wzxy #-}
+
+_wzyx f = _xyzw $ \(V4 a b c d) -> f (V4 d c b a) <&> \(V4 d' c' b' a') -> V4 a' b' c' d'
+{-# INLINE _wzyx #-}
 
 ew :: R4 t => E t
 ew = E _w