A note on “Methods for constructing distance matrices and the inverse eigenvalue problem”

In this paper, a symmetric nonnegative matrix with zero diagonal and given spectrum, where exactly one of the eigenvalues is positive, is constructed. This solves the symmetric nonnegative eigenvalue problem (SNIEP) for such a spectrum. The construction is based on the idea from the paper Hayden, Re...

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Bibliographic Details
Published in:Linear algebra and its applications 2012-12, Vol.437 (11), p.2781-2792
Main Authors: Jaklič, Gašper, Modic, Jolanda
Format: Article
Language:English
Subjects:
15A18
15A29
Algebra
Euclidean distance matrix
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Perron eigenvector
Sciences and techniques of general use
Symmetric nonnegative inverse eigenvalue problem
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Summary:In this paper, a symmetric nonnegative matrix with zero diagonal and given spectrum, where exactly one of the eigenvalues is positive, is constructed. This solves the symmetric nonnegative eigenvalue problem (SNIEP) for such a spectrum. The construction is based on the idea from the paper Hayden, Reams, Wells, “Methods for constructing distance matrices and the inverse eigenvalue problem”. Some results of this paper are enhanced. The construction is applied for the solution of the inverse eigenvalue problem for Euclidean distance matrices, under some assumptions on the eigenvalues.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2012.06.044