Create matrix using loop?

Question

Here I have a list of numbers (900 numerical values) denoted as d1-1, d1-2, d1-3.....d1-30, d2-1, d2-2, d2-3........d30-30. I want to create a matrix (900x900) which is organized as the below picture. Someone suggested to me that I should use the do loop or while loop. Can you guys help me with this? d1-2 has a magnitude the same as d2-1 but with negative sign.

Answer 1

Symbolic evaluation (if you only need some of the elements of the matrix, use this).

mat[row_, col_] := 
 d[Ceiling[row/30], Ceiling[col/30]] d[Mod[row, 30, 1], Mod[col, 30, 1]]

For instance:

mat[50, 80]
(* d[2, 3] d[20, 20] *)

If you want the actual matrix, just do:

matrix = Array[mat, {900, 900}]

EDIT: If you must use a loop (which is slower), then try this:

matrix = Table[d[Ceiling[row/30], Ceiling[col/30]] d[Mod[row,
   30, 1], Mod[col, 30, 1]], {row, 900}, {col, 900}]

Answer 2

Something like that?

The initial matrix (general case):

mat = Array[d, {30, 30}]; mat // MatrixForm

Gives:

Then:

vec = Flatten[mat]; {vec} // MatrixForm

And finally:

bigmat = Transpose[{vec}].{vec};

Checking:

bigmat[[1]]

bigmat[[;; , 1]]

Diagonal[bigmat]

Answer 3

You don't need a For[] loop. What you need is KroneckerProduct[]:

KroneckerProduct[Array[d, {30, 30}], Array[d, {30, 30}]]