"Loop does not save intermediary steps"
because nothing in your code makes any attempt to save them. Because each diagonal has a different number of elements, probably the simplest storage is to use a cell array:
A = rand(1540,1540);
V = 4:3:size(A,2);
N = numel(V);
C = cell(1,N);
for k = 1:N
C{k} = diag(A,-V(k));
end
All of the diagonals will be in the cell array C:
For example, the 512th diagonal:
V(512)
C{512}
Basic concepts, like how to save data during a loop, are explained in the starting tutorials:
