Spectral Properties Of Small Hadamard Matrices

Keywords

Discrete Fourier transform; Eigenvalues; Gauss sums; Hadamard matrix

Abstract

We prove that if A and B are Hadamard matrices which are both of size 4×4 or 5×5 and in dephased form, then tr(A)=tr(B) implies that A and B 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.

Publication Date

10-1-2016

Publication Title

Linear Algebra and Its Applications

Volume

506

Number of Pages

363-381

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.laa.2016.06.006

Socpus ID

84973537704 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84973537704

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