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% test matrix
>> A = [1 2 3 4 5;
 6 7 8 9 10;
 11 12 13 14 15; 
 16 17 18 19 20;
 21 22 23 24 25]

A =

    1    2    3    4    5
    6    7    8    9   10
   11   12   13   14   15
   16   17   18   19   20
   21   22   23   24   25

% downshift matrix
>> D = [0 0 0 0 1; 1 0 0 0 0; 0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0]
D =

   0   0   0   0   1
   1   0   0   0   0
   0   1   0   0   0
   0   0   1   0   0
   0   0   0   1   0

% downshift test
>> D*A
ans =

   21   22   23   24   25
    1    2    3    4    5
    6    7    8    9   10
   11   12   13   14   15
   16   17   18   19   20

% downshift twice
>>  D*D*A
ans =

   16   17   18   19   20
   21   22   23   24   25
    1    2    3    4    5
    6    7    8    9   10
   11   12   13   14   15

% the trace of downshift is merely upshift
>>  D'
ans =

   0   1   0   0   0
   0   0   1   0   0
   0   0   0   1   0
   0   0   0   0   1
   1   0   0   0   0

% which can be verified as follows:
>> A, D'*A
A =

    1    2    3    4    5
    6    7    8    9   10
   11   12   13   14   15
   16   17   18   19   20
   21   22   23   24   25

ans =

    6    7    8    9   10
   11   12   13   14   15
   16   17   18   19   20
   21   22   23   24   25
    1    2    3    4    5

% putting the input matrix to the left of the downshift matrix.
% then it became a left-shift operation.
>> A*D
ans =

    2    3    4    5    1
    7    8    9   10    6
   12   13   14   15   11
   17   18   19   20   16
   22   23   24   25   21

%% Combining together, D'*A*D is down-and-left shift.
>> D'*A*D
A =

    1    2    3    4    5
    6    7    8    9   10
   11   12   13   14   15
   16   17   18   19   20
   21   22   23   24   25

ans =

    7    8    9   10    6
   12   13   14   15   11
   17   18   19   20   16
   22   23   24   25   21
    2    3    4    5    1