The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Isaac Newton Institute for Mathematical Sciences

The solution of the r-generalized Fibonacci matrix recurrence with noncommutative coefficients

Authors: Maria Anastasia Jivulescu (Department of Mathematics, University Politehnica Timisoara, Romania), Anna Napoli (Departimento di Scienze Fisiche ed Astronomiche, Universita di Palermo, Italia), Antonino Messina (Departimento di Scienze Fisiche ed Astronomiche, Universita di Palermo, Italia)

Abstract

The construction of the general solution of the r-generalized Fibonacci matrix recurrence equation with noncommutative coefficients is reported. The reduction of the general result to the case of commutative coefficients is presented. Our resolutive formula allows the introduction of new permutationally invariant functions of two solvents of a quadratic matrix equation with matrix coefficients, which play the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation.