I am looking for change in eigenvalues as $ p(T)$ is translated as $ p(T+I)$. I thought the following link could be helpful, though I can't figure out any. $T$ being some matrix such that $p(T)=0$
Can the variation in eigenvalues be seen in terms of the polynomial operator 'p' itself? If so, can this be generalized in any sense? Let me know if the question needs clarification. Possible hints or solution will be a great help. Regards.