Root spreads for polynomials and Hermitian matrix pencils Original Research Article

Beginning with a polynomial with real roots, a family of polynomials with degree reduced by one is defined using a nonnegative matrix; then the root spreads of the original polynomial and polynomials in the family are compared. There are applications to the spread of the roots of a Hermitian matrix pencil and the root spreads of its principal subpencils having one fewer row and column.