For pedagogical purposes:

• In general, using Subscripts to define variables is a bad idea in Mathematica. In your problem, I suggest either using k[n] or defining a List ks where each element is one of your matrices.

• Avoid using capital letters when defining variables. All Mathematica built-ins start with capital letters; for instance, K is a reserved symbol in Mathematica, so using it might cause problems.

• There are syntax errors in your For loop. To make it do what you want, here would be the correct syntax:

    Clear[i, k]
    For[i = 1, i <= 5, i++
      , k[i] = {{i, 2*i}, {3*i, 4*i}}
     ]
  

However, in Mathematica, it is often beneficial to avoid loops. Here are a couple of alternatives to the method you've outlined.

• Use Do:

    Do[k[i] = {{i, 2*i}, {3*i, 4*i}}, {i, 1, 5}]
  

• Use a Table to construct a list of k's. You can get parts of lists using [[ <> ]]:

    ks = Table[{{i, 2*i}, {3*i, 4*i}}, {i, 1, 5}];
    ks[[2]]
    (* {{2, 4}, {6, 8}} *)
  

• Use Scan in order to evaluate a function with side effects while avoiding any outputs.

    f[num_] := k[num] = {{num, 2*num}, {3*num, 4*num}}
    Scan[f, {1, 2, 3, 4, 5}]
  

• Take advantage of built-ins and pure functions with Scan:

    Scan[(k[#] = Partition[# Range[4], 2]) &, Range[5]]
  

• Map a function that creates the matrices over a set of inputs:

    ks = Partition[Range[#, 4 #, #], 2] & /@ Range[5]
  

For pedagogical purposes:

• In general, using Subscripts to define variables is a bad idea in Mathematica. In your problem, I suggest either using k[n] or defining a List ks where each element is one of your matrices.

• Avoid using capital letters when defining variables. All Mathematica built-ins start with capital letters; for instance, K is a reserved symbol in Mathematica, so using it might cause problems.

• There are syntax errors in your For loop. To make it do what you want, here would be the correct syntax:

    Clear[i, k]
    For[i = 1, i <= 5, i++
      , k[i] = {{i, 2*i}, {3*i, 4*i}}
     ]
  

However, in Mathematica, it is often beneficial to avoid loops. Here are a couple of alternatives to the method you've outlined.

• Use Do:

    Do[k[i] = {{i, 2*i}, {3*i, 4*i}}, {i, 1, 5}]
  

• Use a Table to construct a list of k's. You can get parts of lists using [[ <> ]]:

    ks = Table[{{i, 2*i}, {3*i, 4*i}}, {i, 1, 5}];
    ks[[2]]
    (* {{2, 4}, {6, 8}} *)
  

• Use Scan in order to evaluate a function with side effects while avoiding any outputs.

    f[num_] := k[num] = {{num, 2*num}, {3*num, 4*num}}
    Scan[f, {1, 2, 3, 4, 5}]
  

• Take advantage of built-ins and pure functions with Scan:

    Scan[(k[#] = Partition[# Range[4], 2]) &, Range[5]]
  

• Map a function that creates the matrices over a set of inputs:

    ks = Partition[Range[#, 4 #, #], 2] & /@ Range[5]