Extracting a 2 x 2 matrix from a 9 x 9 matrix

Question

I have the following code:

For[i = 1, i <= 9, i = i + 8,
  For[j = 1, j <= 9, j = j + 8,
    Print[k[[i, j]]]
  ]
]

The code prints a column of the elements that I want to extract, but I want them as a 2 x 2 matrix. How can I modify my program so it does that?

I want to use For-loops to form the 2 x 2 matrix.

Answer 1

Contrived test data.

m1 = Array[k, {9, 9}]

{{k[1, 1], k[1, 2], k[1, 3], k[1, 4], k[1, 5], k[1, 6], k[1, 7], k[1, 8], k[1, 9]}, 
 ... 
 {k[9, 1], k[9, 2], k[9, 3], k[9, 4], k[9, 5], k[9, 6], k[9, 7], k[9, 8], k[9, 9]}}

Here is how to solve your problem with For-loops. m2 will be the matrix you want. You can substitute any 9 x 9 matrix for m1 and the code will still work.

m2 = ConstantArray[0, {2, 2}];
For[i = 1; ii = 1, i <= 9, i += 8; ii += 1,
  For[j = 1; jj = 1, j <= 9, j += 8; jj += 1,
    m2[[ii, jj]] = m1[[i, j]]]];
m2 // MatrixForm

But really, wouldn't it be simpler just to write

m2 = {m1[[1, 1]], m1[[1, 9]], m1[[9, 1]], m1[[9, 9]]}

or

m2 = {m1[[1, 1]], m1[[1, -1]], m1[[-1, 1]], m1[[-1, -1]]}

or perhaps

m2 = Extract[m1, Tuples[{1, 9}, 2]]

or

m2 = Extract[m1, Tuples[{1, -1}, 2]]

Answer 2

There are different ways to achieve this. The solution differs based on what one wants exactly. If the element's positions are combinations of m and n in the list, the crude way of achieving this is:

Table[t[[i,j]],{i,{m,n}},{j,{m,n}}]

In the above, t is the list that contains the elements. This will generate the list of the elements required. As the output is required in the matrix form,

Table[t[[i,j]],{i,{m,n}},{j,{m,n}}]//MatrixForm

will print the list in the matrix form.

Update: Let A is the list that contains the extracted elements, B is the identity matrix that has to be added and m and n are the elements in the indices

A=Table[t[[i,j]],{i,{m,n}},{j,{m,n}}] (*extracts the elements from the list t from the postions, {m,m},{m,n},{n,m} and {n,n}*)
B=IdentityMatrix[2];  (*generates identity matrix of size 2*)
C=A+B;   (*compltes addition of lists and stores in C *)
Print[MatrixForm[C]]  (*Prints C in the matrix form*)

Answer 3

If you insist in For and something similar to Print then

With[{prnt = WriteString[$Output, ##] &},
 For[i = 1, i <= 9, i = i + 8,
  For[j = 1, j <= 9, j = j + 8,
   prnt[k[[i, j]], " "]
   ];
  prnt["\n"]
  ]
 ]

From the documentation details for Print

With a text-based interface, Print ends its output with a single newline (line feed).

Print sends its output to the channel $Output.

And each Print will be in an independent cell, but we can WriteString to the same $Output using

WriteString[$Output, #] &