Functional identities on matrix algebras

Complete solutions of functional identities $\sum_{k\in K}F_k(\bar{x}m^k)x_k = \sum{l\in L}x_lG_l(\bar{x}_m^l)$onthematrixalgebra$M_n($\mathbb{F}$)$ are given. The nonstandard parts of these solutions turn out to follow from the Cayley-Hamilton identity.