Mathematics Faculty Articles

Title

Partitions of Equiangular Tight Frames

Document Type

Article

Publication Date

8-1-2017

Publication Title

Linear Algebra and its Applications

Keywords

Equiangular tight frames, Grassmannian frames, Conference matrices

ISSN

0024-3795

Volume

526

First Page

95

Last Page

120

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.

Comments

©2017 Elsevier Inc. All rights reserved

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2017.03.022

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