Title: On the matrix $pth$ root functions and generalized Fibonacci sequences,
Abstract: This study is devoted to the polynomial representation of the matrix $p$th
root functions. The Fibonacci-Hörner decomposition of the matrix powers and
some techniques arisen from properties of generalized Fibonacci sequences,
notably the Binet formula, serves as a triggering factor to provide explicit
formulas for the matrix $p$th roots. Special cases and illustrative numerical
examples are given.