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Coprimality of Certain Families of Integer Matrices

Pal, Piya and Vaidyanathan, P. P. (2011) Coprimality of Certain Families of Integer Matrices. IEEE Transactions on Signal Processing, 59 (4). pp. 1481-1490. ISSN 1053-587X. https://resolver.caltech.edu/CaltechAUTHORS:20110606-081745999

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Abstract

Commuting coprime pairs of integer matrices have been of interest in multidimensional multirate systems, and more recently in array processing. In multirate systems they arise, for example, in the design of interchangeable cascades of decimator and expander matrices. In array processing they arise in the construction of dense coarrays from sparse sensors located on a pair of lattices. For the important case of two dimensional signals, these matrices have size 2 × 2. In this paper the condition for coprimality is derived for several classes of 2 × 2 integer matrices, namely circulant, skew-circulant, and triangular families. The first two are also commuting families. For each class, the special case of adjugate pairs, which automatically commute, is also elaborated. It is also shown that the problem of testing coprimality of two 2 × 2 matrices is equvialent to testing coprimality of a pair of triangular matrices, which can be done almost by inspection. Also considered is the case of 3 × 3 triangular matrices and their adjugates, which have potential applications in three dimensional signal processing.


Item Type:Article
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http://dx.doi.org/10.1109/TSP.2010.2103070DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5678658&tag=1PublisherUNSPECIFIED
Additional Information:© 2010 IEEE. Manuscript received June 24, 2010; revised November 03, 2010; accepted December 21, 2010. Date of publication December 30, 2010; date of current version March 09, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Soontorn Oraintara. This work was supported in part by the ONR grant N00014-08-1-0709, and the California Institute of Technology. The authors would like to thank the reviewers for their many useful suggestions.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-08-1-0709
CaltechUNSPECIFIED
Subject Keywords:Adjugate pairs; circulants; commuting matrices; coprime matrices; multidimensional multirate systems; Toeplitz matrices
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INSPEC Accession Number11851216
Issue or Number:4
Record Number:CaltechAUTHORS:20110606-081745999
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110606-081745999
Official Citation:Pal, P.; Vaidyanathan, P.P.; , "Coprimality of Certain Families of Integer Matrices," Signal Processing, IEEE Transactions on , vol.59, no.4, pp.1481-1490, April 2011 doi: 10.1109/TSP.2010.2103070 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5678658&isnumber=5725269
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23908
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Jun 2011 21:47
Last Modified:03 Oct 2019 02:51

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