Computing hypermatrix spectra with the Poisson product formula |
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Authors: | Joshua Cooper |
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Affiliation: | Department of Mathematics, University of South Carolina, Columbia, SC, USA. |
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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 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. |
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Keywords: | hypermatrix spectrum resultant hypergraph |
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