Surjectivity of maps induced on matrices by polynomials and entire functions

Authors

Shubhodip Mondal, Indian Statistical Institute Bangalore

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