Equiangular tight frames from complex Seidel matrices containing cube roots of unity

Details Equiangular tight frames from complex Seidel matrices containing cube roots of unity Equiangular tight frames from complex Seidel matrices containing cube roots of unity

2008-05-14

arxiv.org/abs/0805.2014v2

Mathematics

Functional Analysis

New version comments: A few minor typos corrected. Accepted for publication in Linear Algebra Appl

Scientific paper

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.

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