fun transp ([]::_) = []
| transp [[x:real]] = [[x:real]]
| transp rows =
(map hd rows) :: transp (map tl rows);


infix ++;
local
	fun  addL [] [] = [] |
	addL [x:real]  [y:real] = [x+y]|
	addL (x::xs)  (y::ys) = (x+y) :: addL xs ys
in
   fun [] ++ [] = [] |
	[[x:real]] ++ [[y:real]] = [[x+y]] |
	(x::xs) ++ (y::ys) = addL x y::(xs++ys)
end;

infix **;
local
fun sumMult ([],[]) = 0.0 |
	sumMult ((x::xs),(y::ys)) = x*y + sumMult (xs,ys)
fun mulVec [] [] = []|
	 mulVec [] _ = []|
	 mulVec _ [] = []|
		mulVec [x:real] [[y:real]] = [x*y]|
		mulVec (w::ws) (z::ys) =  sumMult(w::ws,z)::(mulVec (w::ws) ys)

in

   fun  [] ** []= [] |
	    [] ** _ = [] |
	[[x:real]] ** [[y:real]] = [[x*y]] |
	(x::xs) ** b = (mulVec x (transp b)) :: (xs**b)

end;