On the spectra of direct sums and Kronecker products of side length 2 hypermatrices and related algorithmic problems in data science.
We present elementary method for obtaining the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic hypermatrices having side length 2. The method is based on a generalization of Parseval's identity. We use the general formulation of Parseval's identity to introduce hypermatrix Fourier transforms and discrete Fourier hypermatrices. We conclude the talk with illustrations of spectral decompositions of adjacency hypermatrices of finite groups and a proof of a hypermatrix Rayleigh quotient inequality. This is a joint work with Yuval Filmus.