Surjectivity of maps induced on matrices by polynomials and entire functions
Article Type
Research Article
Publication Title
American Mathematical Monthly
Abstract
We 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.
First Page
260
Last Page
264
DOI
10.4169/amer.math.monthly.124.3.260
Publication Date
3-1-2017
Recommended Citation
Mondal, Shubhodip, "Surjectivity of maps induced on matrices by polynomials and entire functions" (2017). Journal Articles. 2653.
https://digitalcommons.isical.ac.in/journal-articles/2653
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