Linear transformations preserving algebraic elements of degree 2

ABSTRACT

In the present paper, we will characterize linear maps of $M_n\left(\mathbb{F}\right)$, the ring of all n × n matrices over an algebraically closed field $\mathbb{F}$ of characteristic zero, which preserve the set of all algebraic elements of degree 2.

Keywords:

• Linear preserver problems
• algebraic elements of degree 2
• nilpotent elements
• symmetric group

AMS Subject Classifications:

• 15A86
• 15A21

Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions. Especially we want to thank the referee for the reorganization of the paper as well as the suggestion of presenting the main result in a series of steps.

Disclosure statement

No potential conflict of interest was reported by the author(s).