How to operate block matrices?

I'd like to operate matrix in which each element is composed by two numbers. For instance,

If I have a matrix B=[1,2; 3,4] for instance, I'd like to have

Someone have some idea?

Thank you!

Answer 1

[Rik]

Perhaps a function like pagemtimes does what you need.

You will have to store your matrix as a 3-D matrix. Even if pagemtimes is not what you want, that will make it easier to write a loop to apply the operation you do want.

[Noemi ZM]

Thank you!!

[Image Analyst]

Can you explain exactly what was multiplied by what, and summed, to get the output matrixes?

Answer 2

[Paul]

One can always store block matrices in cell arrays and then roll code to implement the block matrix algebra. Maybe there is a submittal on the FEX for a block matrix class?

A = {[1 2] , [3 4]; [3 5] , [4 2]};
B = {1 , 2; 3, 4};
C = blockmtimes(B,A) 

C = 2×2 cell array
    {[ 7 12]}    {[ 11 8]}
    {[15 26]}    {[25 20]}

function C = blockmtimes(A,B)
[m,n] = size(A);
[n,s] = size(B);
for ii = 1:m
    for jj = 1:n
        C{ii,jj} = zeros(size(A{ii,jj},1),size(B{ii,jj},2));
        for kk = 1:n
            C{ii,jj} = C{ii,jj} + A{ii,kk}*B{kk,jj};
        end
    end
end
end

[Noemi ZM]

Great idea, thank you!