In the original question and the image you mentiones 2x2 submatrices. In the commend you talk of 4x4 submatrices. This is not clear in this sentence also:
These 4x4 matrices are unique; i.e., I have to take the first two elements of the first row and same elements of the second row and average it.
Here I used n=4, but perhaps you want n=2:
n = 4;
X = rand(100, 100);
Y = reshape(X, [n, 100/n, n, 100/n]);
Y = permute(Y, [2, 4, 1, 3]);
Y = reshape(Y, [100/n, 100/n, n*n]);
Result = mean(Y, 3);
Best Answer