On the spectra of direct sums and Kronecker product constructions

Edinah K. Gnang and Yuval Filmus
Linear Algebra and its Applications, Volume 519, 2017, pp. 238–277

We study the spectral theory of hypermatrices, initiated by Gnang, Elgammal and Retakh.

Here are some of our results:

  • We show that Hadamard hypermatrices of side length 2 exist unless the order is an even number larger than 2.
  • We determine the characteristic polynomial and hyperdeterminant of matrices of side length 2.
  • We generalize the Rayleigh quotient to hypermatrices.


 author = {Edinah K. Gnang and Yuval Filmus},
 title = {On the spectra of direct sums and {K}ronecker product constructions},
 journal = {Linear Algebra and its Applications},
 volume = {519},
 pages = {238--277},
 year = {2017}
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