Nonderogatory matrices as sums of p-potent and nilpotent matrices

2025/08/13 by Pojar, Andrada
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.10079

Abstract

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, such that E^p=E, and V³=0.

Citations

• Companion matrices as sums of p-potent and nilpotent matrices
• Decompositions of Matrices into Potent and Square-Zero Matrices
• Nil-clean companion matrices
• Nil-clean matrix rings
• Nil clean rings
• Lifting idempotents and exchange rings

Related

• m-nil-clean nonderogatory matrices
• Companion matrices as sums of p-potent and nilpotent matrices
• Matrices over finite fields of odd characteristic as sums of diagonalizable and square-zero matrices
• A bound for the nilpotence index associated to m-nil-clean nonderogatory matrices
• Decompositions of Matrices into Potent and Square-Zero Matrices