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Generating New Commuting Coprime Matrix Pairs From Known Pairs

Vaidyanathan, P. P. and Pal, Piya (2011) Generating New Commuting Coprime Matrix Pairs From Known Pairs. IEEE Signal Processing Letters, 18 (5). pp. 303-306. ISSN 1070-9908.

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Commuting coprime integer matrices arise in signal processing in a number of contexts. This paper develops two ways, one nonlinear and the other linear, to generate new commuting coprime pairs from known pairs. The first method is based on computing powers of the initial pair of matrices, and the secondmethod is based on appropriate types of linear combinations of the initial pair of matrices. This enriches the already known families of coprime matrices reported in recent literature. Several properties of the newly generated coprime pairs are also addressed.

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Additional Information:© 2011 IEEE. Manuscript received December 21, 2010; revised February 28, 2011; accepted March 01, 2011. Date of publication March 07, 2011; date of current version March 17, 2011. This work was supported in part by the Office of Naval Research under Grant N00014-08-1-0709, and by the California Institute of Technology. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Yuriy V. Zakharov. The elegant proof of property 5 in Lemma 4 was suggested by an anonymous reviewer, and is considerably simpler than the proof in our original submission.
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Office of Naval Research (ONR)N00014-08-1-0709
Subject Keywords:Adjugate pairs; commuting matrices; coprime arrays; coprime matrices
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INSPEC Accession Number11872960
Issue or Number:5
Record Number:CaltechAUTHORS:20110405-110827968
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Official Citation:Vaidyanathan, P. P.; Pal, P.; , "Generating New Commuting Coprime Matrix Pairs From Known Pairs," Signal Processing Letters, IEEE , vol.18, no.5, pp.303-306, May 2011 doi: 10.1109/LSP.2011.2123887
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23241
Deposited By: Jason Perez
Deposited On:10 Apr 2011 03:59
Last Modified:03 Oct 2019 02:44

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