3 citations · 6 across the 4 of their papers we have counts for
5 papers
Diagonal elements in the Nonnegative Inverse Eigenvalue Problem
Richard Ellard, Helena Šmigoc
We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem…
An extension of the Hermite-Biehler theorem with application to polynomials with one positive root
Richard Ellard, Helena Šmigoc
If a real polynomial is Hurwitz stable (every root if lies in the open left half-plane), then the Hermite-Biehler Theorem says that the polynomials $p(-x^…
Families of Newton-like inequalities for sets of self-conjugate complex numbers
Richard Ellard, Helena Šmigoc
We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first k…
Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem
Richard Ellard, Helena Šmigoc
We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalu…
Constructing New Realisable Lists from Old in the NIEP
Richard Ellard, Helena Šmigoc
Given a list of complex numbers σ:=(λ_1,λ_2,...,λ_m), we say that σ is realisable if σ is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Pr…