Partitions of equiangular tight frames

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–Singe...

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Bibliographic Details
Published in:Linear algebra and its applications 2017-08, Vol.526, p.95-120
Main Authors: Rosado, James, Nguyen, Hieu D., Cao, Lei
Format: Article
Language:English
Subjects:
Algorithms
Conference matrices
Efficiency
Equiangular tight frames
Frames
Grassmannian frames
Linear algebra
Mathematical analysis
Mathematics
Matrix
Matrix methods
Partitions (mathematics)
Symmetry
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.03.022