Speed up my own Orthogonalize and QRDecomposition

Question

I defined Gram-Schmidt like this:

GS[A_] := Module[{u = {}, col, e = {}, ae, t},
  col = Transpose[A];(* lista dos vectores coluna de A *)
  u = Append[u, col[[1]]];
  e = AppendTo[e, u[[1]]/Norm[u[[1]]]];
  For[i = 2, i <=  Length[col], i++, ae = 0; t = 1;
   While[t <= i - 1, ae = ae - (col[[i]].e[[t]])*e[[t]]; t++];
   u = AppendTo[u, col[[i]] + ae];
   e = Append[e, u[[i]]/Norm[u[[i]]]]]; {u, e}]

and I defined a QR decomposition:

QR[A_] := Module[{Ak, i, Q, R = {}, a = {}, col, k},
  Ak = FullSimplify[GS[A]];
  col = Transpose[A];(* lista dos vectores coluna de A *)
  Q = Transpose[Ak[[2]]];
  For[i = 1, i <= Length[Ak[[2]]], i++, a = {}; k = 1;
   While[k <= Length[col], a = AppendTo[a, col[[k]]. Ak[[2]][[i]]]; 
    k++]; 
   R = AppendTo[R, a]];
  R = UpperTriangularize[FullSimplify[R]]; {Q, R}]

I want to do my QR with this matrix:

SJorge = Import[
   StringJoin[
    "https://c2.staticflickr.com/4/3463/3823583611_c80bf5a375_b.jpg"]]\
;
imagem = ColorConvert[SJorge, "Grayscale"];
M = ImageData[imagem, "Byte"];

That have as dimensions {521,1023}. My code runs but doesn't give any values back. I works for normal and short matrixes.

Need Help..Thanks!