Computing hypermatrix spectra with the Poisson product formula

We compute the spectrum of the 'all ones' hypermatrix using the Poisson product formula. This computation includes a complete description of the eigenvalues' multiplicities, a seemingly elusive aspect of the spectral theory of tensors. We also give a distributional picture of the spec...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 63; no. 5; pp. 956 - 970
Main Authors Cooper, Joshua, Dutle, Aaron
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2015
Taylor & Francis Ltd
Subjects
Algebra
Computation
Eigenvalues
Graphs
hypergraph
hypermatrix
Mathematical analysis
Planes
Primary: 15A69
resultant
Secondary: 15A18
Spectra
Spectral theory
spectrum
Tensors
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Summary:We compute the spectrum of the 'all ones' hypermatrix using the Poisson product formula. This computation includes a complete description of the eigenvalues' multiplicities, a seemingly elusive aspect of the spectral theory of tensors. We also give a distributional picture of the spectrum as a point-set in the complex plane. Finally, we use the technique to analyse the spectrum of 'sunflower hypergraphs', a class that has played a prominent role in extremal hypergraph theory.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2014.910207