Equiangular tight frames from complex Seidel matrices containing cube roots of unity
Functional Analysis
2008-09-01 v2 Operator Algebras
Abstract
We derive easily verifiable conditions which characterize when complex Seidel matrices containing cube roots of unity have exactly two eigenvalues. The existence of such matrices is equivalent to the existence of equiangular tight frames for which the inner product between any two frame vectors is always a common multiple of the cube roots of unity. We also exhibit a relationship between these equiangular tight frames, complex Seidel matrices, and highly regular, directed graphs. We construct examples of such frames with arbitrarily many vectors.
Cite
@article{arxiv.0805.2014,
title = {Equiangular tight frames from complex Seidel matrices containing cube roots of unity},
author = {Bernhard G. Bodmann and Vern I. Paulsen and Mark Tomforde},
journal= {arXiv preprint arXiv:0805.2014},
year = {2008}
}
Comments
New version comments: A few minor typos corrected. Accepted for publication in Linear Algebra Appl