Some properties of n-matrix factorizations of polynomials

2023/10/05 by Yves Fomatati, Fomatati, Yves
Computer Science · Engineering · Mathematics · #12D05 #15A23 #16D40 #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Mathematics #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2310.03372

openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R=K[x₁,x₂,⋯, x_m] where K is a field. In this paper, we give some properties of n-matrix factorizations of polynomials in R. We also derive some results giving some lower bounds on the number of n-matrix factors of polynomials. In particular, we give a lower bound on the number of matrix factors of minimal size for the sums of squares polynomial f_m=x₁²+⋯ + x_m² for m=8.

Related

• Roots multiplicity and square-free factorization of polynomials using\n companion matrices
• Factorization of composed polynomials and applications
• On 3-matrix factorizations of polynomials
• Refined multiplicative tensor product of matrix factorizations
• The number of matrices over \mathbbF_q with irreducible characteristic polynomial