Article
Partitions of Equiangular Tight Frames
Linear Algebra and its Applications
Document Type
Article
Publication Date
8-1-2017
Keywords
- Equiangular tight frames,
- Grassmannian frames,
- Conference matrices
Disciplines
Abstract
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.
ORCID ID
0000-0001-7613-7191
ResearcherID
G-7341-2019
DOI
10.1016/j.laa.2017.03.022
Citation Information
James Rosado, Hieu D. Nguyen and Lei Cao. "Partitions of Equiangular Tight Frames" Linear Algebra and its Applications Vol. 526 (2017) p. 95 - 120 ISSN: 0024-3795 Available at: http://works.bepress.com/lei-cao/14/
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