Surjectivity of maps induced on matrices by polynomials and entire functions

2015/03/13 by Mondal, Shubhodip
#15A16 #30D20 #Complex Variables (math.CV) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1503.04209

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 M_n(k) for n ≥ 2. The criterion is given in terms of critical points and uses simple linear algebra. Following that, we formulate and prove a corresponding result for entire functions as well.

Related

• Surjectivity of polynomial maps on Matrices
• On the injectivity of evaluation maps induced by polynomials on certain algebras
• Polynomial Maps with Constants over Division Algebras and the Generalized Kaplansky--L'vov Conjecture
• Images of polynomial maps with constants
• Matrix identities with forms