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

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Sarala Gurijala 2022-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/1719300-how-to-create-a-matrix-with-matrices-as-elements-where-the-matrix-a-contains-symbolic-variables

评论： Voss 2022-5-19

采纳的回答： Voss

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dpb 2022-5-14

编辑：dpb 2022-5-15

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 2022-5-15

Thank you

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Answer 1

Voss 2022-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/1719300-how-to-create-a-matrix-with-matrices-as-elements-where-the-matrix-a-contains-symbolic-variables#answer_964040

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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