Maximum robustness and surgery of frames in finite dimensions

We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and surgery of frames. We also answer the question of when length surg...

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Bibliographic Details
Published in:	Linear algebra and its applications Vol. 439; no. 5; pp. 1330 - 1339
Main Authors:	Copenhaver, Martin S., Kim, Yeon Hyang, Logan, Cortney, Mayfield, Kyanne, Narayan, Sivaram K., Sheperd, Jonathan
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-09-2013
Subjects:	Diagram vectors Erasures Frames Gramian operator Length surgery Redundancy Robustness Subframes Surgery Tight frames Frames Erasures Redundancy 05B20 15A03 Tight frames Gramian operator Diagram vectors Surgery Subframes Robustness Length surgery Primary 42C15
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Summary:	We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and surgery of frames. We also answer the question of when length surgery resulting in a tight frame set for Hn is possible.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2013.04.016