In this paper, we exhibit two matrix representations of the rational roots of
generalized Fibonacci polynomials (GFPs) under convolution product, in terms of
determinants and permanents, respectively. The underlying root formulas for
GFPs and for weighted isobaric polynomials (WIPs), which appeared in an earlier
paper by MacHenry and Tudose, make use of two types of operators. These
operators are derived from the generating functions for Stirling numbers of the
first kind and second kind. Hence we call them Stirling operators. To construct
matrix representations of the roots of GFPs, we use the Stirling operators of
the first kind. We give explicit examples to show how the Stirling operators of
the second kind appear in the low degree cases for the WIP-roots. As a
consequence of the matrix construction, we have matrix representations of
multiplicative arithmetic functions under the Dirichlet product into its
divisible closure.Comment: 13 page