A theorem of Boyle and Handelman gives necessary and sufficient conditions for an
-tuple
of nonzero complex numbers to be the nonzero spectrum of some matrix with
nonnegative entries, but is not constructive and puts no bound on the necessary
dimension of the matrix. Working with polynomial matrices, we constructively
reprove this theorem in a special case, with a bound on the size of the polynomial
matrix required to realize a given polynomial.
Keywords
nonnegative matrices, eigenvalues, power series,
nonnegative inverse eigenvalue problem