Centrosymmetric nonnegative realization of spectra

Symmetric nonnegative realization of spectra

A perturbation result, due to R. Rado and presented by H. Perfect in 1955, shows how to modify r eigenvalues of a matrix of order n, r ≤ n, via a perturbation of rank r, without changing any of the n − r remaining eigenvalues. This result extended a previous one, due to Brauer, on perturbations of rank r = 1. Both results have been exploited in connection with the nonnegative inverse eigenvalue...

Nonnegative realization of complex spectra

On nonnegative realization of partitioned spectra

We consider partitioned lists of real numbers Λ = {λ1, λ2, . . . , λn}, and give efficient and constructive sufficient conditions for the existence of nonnegative and symmetric nonnegative matrices with spectrum Λ. Our results extend the ones given in [R.L. Soto and O. Rojo. Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem. Linear Algebra Appl., 416:844– 856, 2006....

Centrosymmetric and pseudo-centrosymmetric structures refined as non-centrosymmetric.

The behaviour of the Flack parameter for centrosymmetric and pseudo-centrosymmetric crystal structures based on crystal structures published as being non-centrosymmetric is presented. It is confirmed for centrosymmetric structures that the value obtained for the Flack parameter is critically dependent on the Friedel coverage of the intensity data, approaching 0.5 for a coverage of 100% and stic...

The Spectra of Nonnegative Integer Matrices via Formal Power Series

An old problem in matrix theory is to determine the n-tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries (see [BP94, Chapter 4] or [Min88, Chapter VII]). Authors have studied the case where the ntuple is comprised of real numbers [Bor95, Cia68, Fri78, Kel71, Per53, Sal72, Sou83, Sul49], the case where the matrices under consideration are symmetric [Fi...