Partitions of equiangular tight frames

James Rosado, Hieu D. Nguyen, Lei Cao

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)95-120
Number of pages26
JournalLinear Algebra and Its Applications
Volume526
DOIs
StatePublished - Aug 1 2017

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis
  • Algebra and Number Theory

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