How to create a matrix with matrices as elements? where the matrix A contains symbolic variables

[Star Strider]

Use the Symbolic Math Toolbox to create:

syms A B C i p 
A = sym('A',[2 2]);
B = sym('B',[2 1]);
C = sym('C',[1 2]);
E(p) = symsum(C*(A^i)*B,i,0,p)                          % Individual Matrix Element

The matrix is obviously lower triangular, however it is not obvious (to me) how the value of p is defined in each column.

.

[dpb]

Pretty much just write the terms in an array - the products are all 1x1 so the summations are as well.

You'll have to define what P is and have a routine that computes the number of terms to fill in the right number of zeros -- and it's certainly not unambiguous what might be the intermediary ... terms going from third row to last. It may be possible to infer from the context from which this was extracted, but not on its own.

[Sarala Gurijala]

Thank you

Answer 1

[Voss]

It may be useful to see the fact that, for matrices A, B, and C of the given sizes, the products C*B, C*A*B, C*A^2*B, etc., are all scalars, so any sum of those products is a scalar. Therefore, all those expressions are actually scalars, so it's not in fact a matrix of matrices like it seems to be at first glance.

Each of those scalars can be calculated in a for loop to perform the summation:

A = [1 2; 3 4];
B = [1; 2];
C = [1 2];

p = 7;
m = 5;

M = zeros(p,m);
for kk = 1:p % loop over rows
    for jj = 1:m % loop over columns
        for ii = 0:kk-jj % summation loop for element kk,jj
            % note that kk<jj gives "for i = []", so this loop doesn't 
            % execute when kk<jj, and M(kk,jj) remains at 0.
            % kk<jj  corresponds to the upper triangular part of M, 
            % which should be all zeros, so that works out nicely.
            M(kk,jj) = M(kk,jj) + C*A^ii*B;
        end
    end
end
M

M = 7×5

5 0 0 0 0 32 5 0 0 0 177 32 5 0 0 956 177 32 5 0 5141 956 177 32 5 27624 5141 956 177 32 148409 27624 5141 956 177

[Sarala Gurijala]

thank you for your response

[Sarala Gurijala]

But, In my problem Matrix A has the symabolic variables, then what changes should I do. suggest me

Thanks in advance for once again

[Voss]

Maybe the first comment on the question provides some insight.