Let ($k$,$D$) be a differential field. Consider a square matrix $A$ with entries in $k$. We say that $A$ is $D$-similar to $A'$ if and only if there exists an invertible matrix $S$ such that $A$ = $S^{-1}A'S$ + $S^{-1}D(A)$ Does there exist any result in the literature relating the eigenvalues of $A$ with those of $A'$? I have been looking for such a result, but haven't been able to find it.
Thanks in advance