Computing Hypermatrix Spectra with the Poisson Product Formula

Joshua Cooper; Aaron Dutle

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arXiv · 1301.4590

Computing Hypermatrix Spectra with the Poisson Product Formula

Joshua Cooper·Aaron Dutle

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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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BibTeX RIS

Joshua Cooper, Aaron Dutle. 2013-01-19. Computing Hypermatrix Spectra with the Poisson Product Formula. https://arxiv.org/abs/1301.4590

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