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Mathematical Citation Quotient (MCQ) 2017: 0.20

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Lucas Numbers and Determinants

Alireza Moghaddamfar
  • Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
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/ Hadiseh Tajbakhsh
Published Online: 2012-01-24 | DOI: https://doi.org/10.1515/integ.2011.081


In this article, we present two infinite dimensional matrices whose entries are recursively defined, and show that the sequence of their principal minors form the Lucas sequence, that is (2,1,3,4,7,...). It is worth mentioning that to construct these matrices we use nonhomogeneous recurrence relations.

Keywords.: Determinant; Principal Minor; Matrix Factorization; Lucas Sequence; Nonhomogeneous Recurrence Relation; Toeplitz Matrix

About the article

Received: 2010-04-04

Revised: 2011-05-09

Accepted: 2011-05-27

Published Online: 2012-01-24

Published in Print: 2012-02-01

Citation Information: Integers, Volume 12, Issue 1, Pages 21–51, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.081.

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