ON A CLASSIC EXAMPLE IN THE NONNEGATIVE INVERSE EIGENVALUE PROBLEM

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ON A CLASSIC EXAMPLE IN THE NONNEGATIVE INVERSE EIGENVALUE PROBLEM (2008)

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by Thomas J. Laffey , Helena Smigoc

Citations:

2 - 2 self

BibTeX

@MISC{Laffey08ona,
    author = {Thomas J. Laffey and Helena Smigoc},
    title = {ON A CLASSIC EXAMPLE IN THE NONNEGATIVE INVERSE EIGENVALUE PROBLEM },
    year = {2008}
}

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Abstract

This paper presents a construction of nonnegative matrices with nonzero spectrum τ =(3+t, 3 − t, −2, −2, −2) for t>0. The result presented gives a constructive proof of a result of Boyle and Handelman in this special case. This example exhibits a surprisingly fast convergence of the spectral gap of τ to zero as a function of the number of zeros that are added to the spectrum.

Keyphrases

nonzero spectrum constructive proof fast convergence spectral gap special case nonnegative matrix

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