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Jan 10, 2022 at 12:08 comment added Daniel Huber I made an update for this case. Note instead of using "Times" I use "**", that is "NonCommutatvve Multiply". This is necessary because otherwise MMA will reorder the terms.
Jan 10, 2022 at 12:07 history edited Daniel Huber CC BY-SA 4.0
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Jan 10, 2022 at 11:50 comment added AlbertLew Furthermore, Daniel, your solution looks impressive, but it does not work in my case, where the matrices are made of symbolic matrix blocks or symbolic sub matrices like X and Y in my post, and the specific values for each entry in those sub matrices is unknown, what I am doing is pure symbolic calculations.
Jan 10, 2022 at 11:35 comment added AlbertLew Thanks Daniel. By default, mathematica identifies each matrix as one constituting of scalars. So when two matrices make dot produce, the Dot[] will employ Times[] to work out the result entry by entry, that is why when the matrices are made of symbolic matrix blocks or symbolic sub matrices, it is hard to teach mathematica to do the product correctly without commutation.
Jan 10, 2022 at 10:38 history answered Daniel Huber CC BY-SA 4.0