How to multiply a (2 by 2) matrix M with M [i.e M*M'] where the elements of the matrix M are also matrices ?

%Here is my problem. Which can be directly copied in Matlab.

clc;
x=1:5;
y=6:10;
[x,y]=meshgrid(x,y);% i.e x and y are matrices.

%I have some coefficients

a1=0.2;  a2=.5;  a3=0.2;  a4=0.4;

%Now the matrix is:

M=[a1.*x a2.*y; a3.*x a4.*y]

%How to get Newmatrix =M*M' ?

%The new matrix must have 4 submatrices in the form of M11 M12 M21 and M22?

   %I did following: 

M=[a1.*x a2.*y; a3.*x a4.*y];

A= M*M';

AA = mat2cell(A,repmat(5,2,1), repmat(5,2,1));

M11=cell2mat(AA(1))

M12=cell2mat(AA(3))

M21=cell2mat(AA(2))

M22=cell2mat(AA(4))

%However, these outputs are not correct. How to correct it? I suspect that the x and y when multiplied or squired should be element-wise (.i.e. x.^2 ) but I could not manage to do that in Matlab.

Answer 1

[Thorsten]

M={a1.*x, a2.*y; a3.*x, a4.*y};
A = cellfun(@(x) x*x', M, 'UniformOutput', false);