14-84 Dynneson

Tensor polytopes, Hom polytopes, Hyper-matrices and data clustering (2941K, .pdf) Dec 6, 14

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Abstract. Expected quantities are presented for the facets of the Tensor-polytope and the number of vertices of the Hom-polytope, for regular polygons as inputs. A cluster analysis was performed on the resulting data. The clustering scripts are provided to aid in reproducing the method and furthering the results. The concept of the standard matrix is extended to arbitrary dimensionality resulting in Hyper-matrices. The Hypercube matrix is used to represent Tensors, and has numerous potential applications in physics and various fields of research such as finance and statistics.

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