Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem
Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem
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DOI：
10.1016/j.laa.2015.10.035
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Richard Ellard;Helena vSmigoc
中科院分区：
文献类型：
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作者：
Richard Ellard;Helena vSmigoc
我们说一个实数列表是“对称可实现的”，如果它是某个(入口式)非负对称矩阵的谱。对称非负反特征值问题是刻画所有对称可实现列表的问题，本文提出了一种构造对称可实现列表的递归方法。我们得到的可实现族的性质允许我们在四十年来从Fiedler在1974年的工作开始发展起来的许多充分条件之间建立几个新的联系。我们证明了基本上所有已知的充分条件都包含在我们引入的族中或等价于我们引入的族。
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.