Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897727 | Linear Algebra and its Applications | 2018 | 14 Pages |
Abstract
The nonnegative inverse eigenvalue problem (NIEP) is to characterize the spectra of entrywise nonnegative matrices. A finite multiset of complex numbers is called realizable if it is the spectrum of an entrywise nonnegative matrix. Monov conjectured that the kth-moments of the list of critical points of a realizable list are nonnegative. Johnson further conjectured that the list of critical points must be realizable. In this work, Johnson's conjecture, and consequently Monov's conjecture, is established for a variety of important cases including Ciarlet spectra, SuleÄmanova spectra, spectra realizable via companion matrices, and spectra realizable via similarity by a complex Hadamard matrix. Additionally we prove a result on differentiators and trace vectors, and use it to provide an alternative proof of a result due to Malamud and a generalization of a result due to Kushel and Tyaglov on circulant matrices. Implications for further research are discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sarah L. Hoover, Daniel A. McCormick, Pietro Paparella, Amber R. Thrall,