A new approach to Bezout equations derived from multivariate polynomial matrices and real entire functions

DOI10.1080/03081087.2015.1008969zbMath1334.15045OpenAlexW2065697290MaRDI QIDQ3455685

Koichi Suyama, Nobuko Kosugi

Publication date: 11 December 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2015.1008969

zbMATH Keywords

Gröbner basesentire functionBézout equationprimenessmultivariate polynomial matrixmultivariate rational function matrices

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Polynomials, factorization in commutative rings (13P05) Matrix exponential and similar functions of matrices (15A16) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• SINGULAR

Cites Work

• New coprimeness over multivariable polynomial matrices and its application to control delay systems
• On explicit solutions to the Bezout equation
• Small degree solutions for the polynomial Bezout equation
• A formal theory of matrix primeness
• Topics in multidimensional linear systems theory
• Extensions of some results of P. Humbert on Bezout's identity for classical orthogonal polynomials
• Effective Bezout identities in \({\mathbb{Q}}[z_ 1,\dots ,z_ n\)]
• Divisibility properties of integral functions
• Notes on n-Dimensional System Theory
• Bezout equations over bivariate polynomial matrices related by an entire function
• Gröbner bases and systems theory

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