Computing Hypermatrix Spectra with the Poisson Product Formula

2013/01/19 by Cooper, Joshua, Dutle, Aaron · 2 citations
#05C65 #FOS: Mathematics #Primary 15A69 #Secondary 15A18 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1301.4590

Abstract

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 general distributional picture of the spectrum as a point-set in the complex plane, and use our techniques to analyze the spectrum of "sunflower hypergraphs", a class that has played a prominent role in extremal hypergraph theory.

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