Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem

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 Eigenvalue Problem (SNIEP) is the problem of characterising all symmetrically realisable lists. In this paper, we present a recur...

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Bibliographic Details
Published in:Linear algebra and its applications 2016-06, Vol.498, p.521-552
Main Authors: Ellard, Richard, Šmigoc, Helena
Format: Article
Language:English
Subjects:
Nonnegative matrices
Soules matrix
Symmetric Nonnegative Inverse Eigenvalue problem
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Summary: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 Eigenvalue Problem (SNIEP) is the problem of characterising all symmetrically realisable lists. In this paper, we present a recursive method for constructing symmetrically realisable lists. The properties of the realisable family we obtain allow us to make several novel connections between a number of sufficient conditions developed over forty years, starting with the work of Fiedler in 1974. We show that essentially all previously known sufficient conditions are either contained in or equivalent to the family we are introducing.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2015.10.035