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

By Bernhard G. Bodmann, Vern I. Paulsen, M. Tomforde. 2008

63 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/41ffc88146dd11e4122ccdcec4f4bfcc0847c633

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In Applied Mathematics

In Mathematical Physics

Ferenc SzollHosi

Citations in the corpus

Steiner equiangular tight frames (2010, background): “Some of this theory generalizes to the complexvariable setting in the guise of complex Seidel matrices [3, 5, 14].”
On the construction of equiangular frames from graphs (2009, background): “Understanding the subfield of the complex numbers the entries of the signature matrix can or must come from may be pivotal in understanding complex equiangular tight frames (cf [K06], [STDH07], [BPT08]).”
Construction, classification and parametrization of complex Hadamard matrices (2011, background): “This, however, still left unanswered an earlier question from [13], namely whether or not an equiangular (36, 21) frame, whose signature matrix is composed from cubic root of unity exists.”