Partitions of Equiangular Tight Frames
Linear Algebra and its Applications
Equiangular tight frames, Grassmannian frames, Conference matrices
We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison–Singer problem. In particular, we prove that certain diagonal partitions of complex ETFs generated by recursive skew-symmetric conference matrices yield a refinement of the MSS bound. Moreover, we prove that all partitions of ETFs whose largest subset has cardinality three or less also satisfy the MSS bound.
Rosado, James; Nguyen, Hieu D.; and Cao, Lei, "Partitions of Equiangular Tight Frames" (2017). Mathematics Faculty Articles. 273.