For each nonnegative integer $k$, you could find the possible tuples of matrices $(A_1, ..., A_k)$ as follows:
for each of -1, 0, 1, find the ways to write it
as a sum of $k$ summands each in {-1, 0, 1}.
the target matrix $M$ has $n^2$ entries $m_{i, j}$; so the $(A_1, ..., A_k)$ are obtained by combining all the possible ways to get each entry.
First of all apologies for replying very late as I was busy with some other things and I logged again yesterday only after so many months. I am really sorry for that. Yes, your idea of finding ways to write -1,0,1 as k summands of {-1,0,1} appears to be very good. i will try to make the code accordingly. Thanks a lot.
Asked: 2022-01-06 16:25:20 +0100
Seen: 279 times
Last updated: Jan 07 '22
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Do you require the matrices $A_j$ to be pairwise distinct?
That way there would be finitely many tuples of matrices $A_j$ summing to M.
One could also forbid having $A_j = 0$ for any $j$, and forbid having $A_j = -A_k$ for any $j$ and $k$.
Homework ?
Question refined at Ask Sage question 63305.