Companion matrices as sums of p-potent and nilpotent matrices

2025/08/12 by Pojar, Andrada · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.09276

Abstract

We prove that, over a field \mathbbF 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 and only if the trace of C is an integer multiple of unity of \mathbbF.

Citations

• 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

Cited by

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

Related

• Nil-clean companion matrices
• Nonderogatory matrices as sums of p-potent and nilpotent matrices
• m-nil-clean nonderogatory matrices
• Companion Weakly Periodic Matrices over Finite and Countable Fields
• Sums Of K-potent Matrices