The Composition of Polynomials is a Determinant

2021/12/22 by Sergio A. Carrillo
Computer Science · Mathematics · #Matrix Theory and Algorithms #Polynomial and algebraic computation #Mathematics and Applications

paper · doi:10.1080/00029890.2022.2005390

Abstract

We show that the composition of two univariate polynomials can be written as a characteristic polynomial using a block-companion matrix. This matrix is useful to determine whether a polynomial is the composition of two other polynomials. Moreover, it provides bounds for the moduli of roots of such polynomials in the complex case.

Related

• A matrix representation of composition of polynomial maps
• A polynomial generalization of the power-compositions determinant
• The characteristic polynomial and determinant are not ad hoc constructions
• Determinants and Compositions of Natural Numbers
• Questions about determinants and polynomials