I have a series matrices and would like to compute the sum for each $n$. For real and square matrices $A$ and $B$, the series is given as
$$S(n)=A+BAB^\top+B^2A(B^\top)^2+\cdots+B^nA(B^\top)^n.$$
I know that the power of $B$ can be easily computed by eigendecomposition, but I do not know if this can be simplified further. Or if there are any tricks for computing $S(n)$ in R. I appreciate any help!
2026-04-01 09:52:50.1775037170
Simplifications of sum of matrices
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