1) Extract submatrices, 2) vectorize and then 3) put back

Question

I simplify my problem, let says I have three matrices.

I want to extract the red-boxed sub-matrices. I define

S = [1 4;
     2 5]

Answer 1

Assuming that your A, B and C matrices have the same dimensions, rather work with a 3D matrix.

e.g. assuming your example matrices

M = cat(3,A,B,C)

No to extract those 4 upper left elements:

M_subset = M(1:2,1:2,:)

And then to reshape them into the vector you had:

V = M_subset(:)

then manipulate it to get V_new and finally put it back in the original:

M(1:2,1:2,:) = reshape(V_new,2,2,[])