On determinants and inverses of some triband Toeplitz matrices with permuted columns

Volume 20, Issue 3, pp 196--206 http://dx.doi.org/10.22436/jmcs.020.03.02

Publication Date: November 15, 2019 Submission Date: August 13, 2019 Revision Date: October 11, 2019 Accteptance Date: October 28, 2019

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Authors

Pingyun Li - School of Mathematics and Statistics, Linyi University, Linyi 276000, China. Zhaolin Jiang - School of Mathematics and Statistics, Linyi University, Linyi 276000, China. Yanpeng Zheng - School of Automation and Electrical Engineering, Linyi University, Linyi 276000, China.

Abstract

In this paper, we study the triband Toeplitz and Hankel matrices with permuted columns. We obtain expressions for the determinants and the inverses of the triband Toeplitz and Hankel matrices with permuted columns by the Sherman-Morrison-Woodbury formula, where the Pell numbers play an essential role.

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Keywords

• Determinant
• inverse
• Laplace theorem
• Pell number
• triband Toeplitz matrices with permuted columns
• Sherman-Morrison-Woodbury

MSC

•  15A09
•  15A15
•  15B05
•  65F40

References

• [1] E. L. Allgower, Exact inverses of certain band matrices, Numer. Math., 21 (1973/74), 279--284
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] E. H. Bareiss, Computational solutions of matrix problems over an integral domain, J. Inst. Math. Appl., 10 (1972), 68--104
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] M. Bicknell, A primer on the Pell sequence and related sequences, Fibonacci Quart., 13 (1975), 345--349
  • View Article
  • MathSciNet
  • MATH


• [4] M. EI-Mikkawy, A. Karawia, Inversion of general tridiagonal matrices, Appl. Math. Lett., 19 (2006), 712--720
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] C. F. Fischer, R. A. Usmani, Properties of some tridiagonal matrices and their application to boundary value problems, SIAM J. Numer. Anal., 6 (1969), 127--142
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] G. H. Golub, C. F. Van Loan, Matrix Computations, The John Hopkins University Press, Baltimore (1996)
  • MathSciNet
  • Google Scholar


• [7] W. D. Hoskins, P. J. Ponzo, Some properties of a class of band matrices, Math. Comp., 26 (1972), 393--400
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] J. T. Jia, S. M. Li, On the inverse and determinant of general bordered tridiagonal matrices, Comput. Math. Appl., 69 (2015), 503--509
  • View Article
  • MathSciNet
  • Google Scholar


• [9] C. M. Jiang, F. F. Zhang, T. X. Li, Synchronization and Antisynchronization of N-coupled Fractional-Order Complex Chaotic Systems with Ring Connection, Math. Methods Appl. Sci., 41 (2018), 2625--2638
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] T. Koshy, Pell and Pell-Lucas numbers with applications, Springer, New York (2014)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] R. P. Mentz, On the inverse of some conariance matrices of Toeplitz type, SIAM J. Appl. Math., 31 (1976), 426--437
  • View Article
  • Google Scholar


• [12] T. S. Papatheodorou, Inverses for a class of banded matrices and applications to piecewise cubic approximation, Comput. Appl. Math., 8 (1982), 285--288
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] L. Rehnqvist, Inversion of certain symmetric band matrices, Nordisk Tidskr. Informationsbehandling (BIT), 12 (1972), 90--98
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] P. A. Roebuck, S. Barnett, A survey of Toeplitz and releated matrices, Internat. J. Systems Sci., 9 (1978), 921--934
  • View Article
  • Google Scholar


• [15] W. F. Trench, Inversion of Toeplitz band matrices, Math. Comp., 28 (1974), 1089--1095
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] T. Yamamoto, Y. Ikebe, Inversion of band matrices, Linear Algebra Appl., 24 (1979), 105--111
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] M. Yasar, D. Bozkurt, Another proof of Pell identities by using the determinant of tridiagonal matrix, Appl. Math. Comput., 218 (2012), 6067--6071
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] Y. Yazlik, N. Taskara, A note on generalized $k$-Horadam sequence, Comput. Math. Appl., 63 (2012), 36--41
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] F. Yilmaz, D. Bozkurt, Hessenberg matrices and the Pell and Perrin numbers, J. Number Theory, 131 (2011), 1390--1396
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH