Andrada Pojar

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math.RA2026

A bound for the nilpotence index associated to $m$ -nil-clean nonderogatory matrices

Andrada Pojar

It is proved that if $F$ is a field of positive characteristic $p,$ and if $m$ and $n$ are positive integers such that $m \geq 2,$ and $4 \leq n \leq p \leq mn - 1,$ for every $n…

math.RA2025

Nonderogatory matrices as sums of $p$ -potent and nilpotent matrices

Andrada Pojar

We prove that every nonderogatory matrix $A$ over a field of positive odd characteristic $p,$ that is sum of a $p$ -potent matrix and a nilpotent matrix, has a decomposition $A=E+V,…

math.RA2025

Companion matrices as sums of $p$ -potent and nilpotent matrices

Andrada Pojar

We prove that, over a field $F$ of odd characteristic $p$ , a companion matrix $C$ is the sum of $E$ and $N$ , with $E$ $p$ -potent (i.e. $E^{p} = E$ ,) and $N$ nilpotent, if an…

A bound for the nilpotence index associated to m-nil-clean nonderogatory matrices

Nonderogatory matrices as sums of p-potent and nilpotent matrices

Companion matrices as sums of p-potent and nilpotent matrices

A bound for the nilpotence index associated to $m$ -nil-clean nonderogatory matrices

Nonderogatory matrices as sums of $p$ -potent and nilpotent matrices

Companion matrices as sums of $p$ -potent and nilpotent matrices