Array is no good man! Quad Tree matrices perform much nicer from what I've seen. I wrote some matrix stuff based on D. Stott Parker's "Randomized Gaussian elimination" papers (http://www.cs.ucla.edu/~stott/ge/). He presents some recursive block based methods of solving without pivoting. I want to upload the full library to Hackage, but it'd be nice to have some people look through it before - mainly because i never took linear algebra heh. QuickCheck seems to be holding things together though. Check these definitions (where the input matrix has been pre-transformed with the butterfly if needed -- revertRBT . invert . applyRBT): gauss (M.Scalar v) = (M.Scalar 1, M.Scalar v) gauss (M.Matrix (a,b,c,d)) = (M.Matrix (l, M.Scalar 0, x, l'), M.Matrix (u, y, M.Scalar 0, u')) where (l,u) = gauss a (l',u') = gauss $ d - (x * y) x = c * (invert u) y = (invert l) * b invert (M.Scalar v) = M.Scalar (1 / v) invert (M.Matrix (a,b,c,d)) = M.Matrix (w,x,y,z) where w = aI - (aIb * y) x = negate $ aIb * z y = negate $ z * caI z = invert $ d - (caI * b) ----------- aI = invert a caI = c * aI aIb = aI * b benchmarked against (in order of speed): 1. Mesa GL math in C called through FFI. 2. Finger tree based port. 3. Mutable array based port. 2 and 3 were scrapped right away. Heres some of the benchmark vs the C version. ------------------------------------ Matrix Inversion - 999999999x ------------------------------------ ------- haskell ------------ ContextSwitches - 224017 First level fills = 0 Second level fills = 0 ETime( 0:00:41.328 ) UTime( 0:00:40.875 ) KTime( 0:00:00.000 ) ITime( 0:00:41.484 ) ---------- C --------------- ContextSwitches - 640016 First level fills = 0 Second level fills = 0 ETime( 0:01:56.109 ) UTime( 0:01:55.359 ) KTime( 0:00:00.000 ) ITime( 0:01:54.328 ) ------------------------------------ Matrix Inversion - 9999999x ------------------------------------ ------- haskell ------------ ContextSwitches - 6204 First level fills = 0 Second level fills = 0 ETime( 0:00:00.687 ) UTime( 0:00:00.421 ) KTime( 0:00:00.000 ) ITime( 0:00:01.031 ) ---------- C --------------- ContextSwitches - 7396 First level fills = 0 Second level fills = 0 ETime( 0:00:01.171 ) UTime( 0:00:01.171 ) KTime( 0:00:00.000 ) ITime( 0:00:01.250 ) ------------------------------------- Matrix multiplication - 999999999x ------------------------------------- ------- haskell ------------ ContextSwitches - 234644 First level fills = 0 Second level fills = 0 ETime( 0:00:42.093 ) UTime( 0:00:41.609 ) KTime( 0:00:00.000 ) ITime( 0:00:42.187 ) ---------- C --------------- ContextSwitches - 228596 First level fills = 0 Second level fills = 0 ETime( 0:00:41.609 ) UTime( 0:00:41.375 ) KTime( 0:00:00.000 ) ITime( 0:00:41.515 )