Nonnegative realizability with Jordan structure

A general method is given for merging blocks in the Jordan canonical form of a nonnegative matrix. As a consequence, results, more general than any prior ones, are given for the universal realizability of spectra, that is, spectra which are realizable by a nonnegative matrix for each possible Jordan...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 587; pp. 302 - 313
Main Authors Johnson, Charles R., Julio, Ana I., Soto, Ricardo L.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.02.2020
American Elsevier Company, Inc
Subjects
Canonical forms
Jordan structure
Linear algebra
Nonnegative matrix
Realizability
Universal realizability
Jordan structure
Nonnegative matrix
Universal realizability
15A18
15A29
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Summary:A general method is given for merging blocks in the Jordan canonical form of a nonnegative matrix. As a consequence, results, more general than any prior ones, are given for the universal realizability of spectra, that is, spectra which are realizable by a nonnegative matrix for each possible Jordan canonical form allowed by the spectrum. In particular, we generalize a classical result due to Minc, regarding positive diagonalizable matrices. For example, any spectrum that is diagonalizably realizable by a nonnegative matrix with mostly positive off-diagonal entries is universally realizable.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.11.016