Surjectivity of Maps Induced on Matrices by Polynomials and Entire Functions
2017
AbstractWe determine a necessary and sufficient condition for a polynomial over an algebraically closed field k to induce a surjective map on matrix algebras Mn(k) for n ≥ 2. The criterion is given in terms of algebraic conditions on the polynomial and the proof uses simple linear algebra. Following that, we formulate and prove a corresponding result for entire functions as well.
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