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I would like to construct a Kronecker sum function in Mathematica that is similar to the answers to this post, but a more generalised construction.

Presume I have a set of $2\times 2$ matrices denoted through the set $\{X,Y,Z\}$. I would like to construct all of the possible $4\times4$ matrices from the direct sum of this set. Some examples are

$$X \oplus Y$$ $$1_2 \oplus X$$ $$1 \oplus X \oplus 1$$

etc, where $1_2$ denotes an identity matrix of dimension $2\times 2$. How can I create a function that can pick out any of these different combinations.

Thanks very much!

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  • $\begingroup$ You perhaps want something like Tuples[] for this: Flatten[Table[Tuples[{i, x, y, z}, k], {k, 2, 4}], 1] $\endgroup$ – J. M.'s technical difficulties Nov 13 '19 at 6:21

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