Mathematica Matrix Diagonalization Function

Diagonalize[A_, exp_] :=
  (
   (* Variables used *)
   n = (Dimensions[A])[[1]];
   Id = IdentityMatrix[n];
   d = Det[A];
   
   (* Print basic information *)
   Print["A = ", (A // MatrixForm)];
   Print["k (Exponent) = ", exp];
   Print["Det(A) = ", d];
   Print["P(\[Lambda]) = ", (P = CharacteristicPolynomial[A, x])];
   
   (* Solve for \[Lambda]'s *)
   
   Print["Solutions for P(x)=0 (Eigenvalues):"];
   tmp = Solve[P == 0, x];
   \[Lambda] = {};
   For[i = 1, i < (n + 1), 
    i++, (val = tmp[[i]][[1]][[2]]; 
     If[MemberQ[\[Lambda], val], , AppendTo[\[Lambda], val]])];
   
   (* Print \[Lambda]'s *)
   
   For[i = 1, i < (Length[\[Lambda]] + 1), i++, 
    Print[Subscript["\[Lambda]", i], " = ", Part[\[Lambda], i]]];
   
   (* Solve for v's *)
   
   Print["Solutions for (A - \[Lambda]I)v=0 (Eigenvectors):"];
   v = {};
   For[i = 1, i < (Length[\[Lambda]] + 1), i++,
    (
     tmp = NullSpace[A - Id*Part[\[Lambda], i]];
     
     (* Split potential multi-column matrices *)
     
     For[j = 1, j < (Dimensions[Transpose[tmp]][[2]] + 1), j++, 
      AppendTo[v, tmp[[j]]]];
     )];
   
   (* Print v's *)
   
   For[i = 1, i < (Length[v] + 1), i++, 
    Print[Subscript["v", i], " = ", Part[v, i] // MatrixForm]];
   
   (* Calculate diagonalization *)
   Si = Transpose[v];
   S = Inverse[Si];
   Dia = MatrixPower[S.A.Si, exp];
   
   (* Print Results *)
   
   Print[Superscript["S", -1], " = ", Si // MatrixForm];
   Print["S = ", S // MatrixForm];
   
   If[exp == 1,
    (
     Print["D = SA", Superscript["S", -1], " = ", Dia // MatrixForm];
     Print["A = ", Superscript["S", -1], "DS = ", 
      Si.Dia.S // MatrixForm];
     ),
    (
     Print[Superscript["D", exp], " = S", Superscript["A", exp], 
      Superscript["S", -1], " = ", Dia // MatrixForm];
     Print[Superscript["A", exp], " = ", Superscript["S", -1], 
      Superscript["D", exp], "S = ", Si.Dia.S // MatrixForm];
     )];
   
   Return[Dia];
   );