2017/03/03 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Computer Science · Engineering · Mathematics · #15A24 #15B33 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1703.01109
openalex publication_date 2017/03/03 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28
Let p and q be polynomials with degree 2 over an arbitrary field \mathbbF. In the first part of this article, we characterize the matrices that can be decomposed as A+B for some pair (A,B) of square matrices such that p(A)=0 and q(B)=0. The case when both polynomials p and q are split was already known. In the first half of this article, we complete the study by tackling the case when at least one of the polynomials p and q is irreducible over \mathbbF. In the second half of the article, we use a similar method to characterize, under the assumption that p(0)q(0) ≠ 0, the matrices that can be decomposed as AB for some pair (A,B) of square matrices such that p(A)=0 and q(B)=0.