Surjectivity of maps induced on matrices by polynomials and entire\n functions

We determine a necessary and sufficient condition for a polynomial over an\nalgebraically closed field $k$ to induce a surjective map on matrix algebras\n$M_n(k)$ for $n \\ge 2$. The criterion is given in terms of critical points and\nuses simple linear algebra. Following that, we formulate and prove a\ncorresponding result for entire functions as well.\n