English

Spectral Properties of Small Hadamard Matrices

Spectral Theory 2014-09-23 v2

Abstract

We prove that if AA and BB are Hadamard matrices which are both of size 4×44 \times 4 or 5×55 \times 5 and in dephased form, then tr(A)=tr(B)tr(A) = tr(B) implies that AA and BB have the same eigenvalues, including multiplicity. We calculate explicitly the spectrum for these matrices. We also extend these results to larger Hadamard matrices which are permutations of the Fourier matrix and calculate their spectral multiplicities.

Keywords

Cite

@article{arxiv.1409.1176,
  title  = {Spectral Properties of Small Hadamard Matrices},
  author = {Dorin Ervin Dutkay and Eric Weber and John Haussermann},
  journal= {arXiv preprint arXiv:1409.1176},
  year   = {2014}
}