The Diagonalizable Nonnegative Inverse Eigenvalue Problem

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Title: The Diagonalizable Nonnegative Inverse Eigenvalue Problem
Authors: Cronin, Anthony
Laffey, Thomas
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Date: 27-Jul-2018
Online since: 2019-04-23T13:49:58Z
Abstract: In this article we provide some lists of real numbers which can be realized as the spectra of nonnegative diagonalizable matrices but which are not the spectra of nonnegative symmetric matrices. In particular, we examine the classical list σ = (3 + t, 3 − t, −2, −2, −2) with t ≥ 0, and show that 0 is realizable by a nonnegative diagonalizable matrix only for t ≥ 1. We also provide examples of lists which are realizable as the spectra of nonnegative matrices, but not as the spectra of nonnegative diagonalizable matrices by examining the Jordan Normal Form.
Type of material: Journal Article
Publisher: De Gruyter
Journal: Special Matrices
Volume: 6
Issue: 1
Start page: 273
End page: 281
Copyright (published version): 2018 the Authors
Keywords: Nonnegative matrixInverse eigenvalue problemSpectral theory
DOI: 10.1515/spma-2018-0023
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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