All complex equiangular tight frames in dimension 3

In this paper we describe some new algebraic features of the Gram matrices of complex Equiangular Tight Frames (ETF). This lead on the one hand to the nonexistence of several low dimensional complex ETFs; and on the other hand to the full algebraic classification of all complex ETFs in C. We use computer aided methods, in particular, Gröbner basis computations to obtain these results. 2000 Mathematics Subject Classification. Primary 05B20, secondary 46L10.

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