| Peer-Reviewed

A Particular Matrix, Its Inversion and Some Norms

Received: 19 February 2015     Accepted: 9 March 2015     Published: 19 March 2015
Views:       Downloads:
Abstract

In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices.

Published in Applied and Computational Mathematics (Volume 4, Issue 2)
DOI 10.11648/j.acm.20150402.13
Page(s) 47-52
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Positive Definite Matrix, Spectral Norm, Hadamard Inverse, Determinant, Block Diagonal

References
[1] M. Akbulak, D. Bouzkurt, On the Norms of Toeplitz Matrices Involving Fibonacci and Lucas Numbers, HACET J MATH STAT, Vol 37,(2) ,(2008), 89-95
[2] M. Akbulak, A. Ipek, Hadamard Exponential Hankel Matrix, Its Eigenvalues and Some Norms, Math. Sci. Lett., Vol 1, No. 1, (2012), 81-87
[3] D. Bozkurt, On the l_p Norms of Almost Cauchy-Toeplitz Matrices, Tr. J. of Mathematics, 20, (1996), 545-552
[4] D. Bozkurt, S. Solak, A Note on Bound for Norms of Cuachy-Hankel Matrices, Numerical Linear Algebra, vol. ED-10, (2003), 377-382
[5] D. Bozkurt, A Note on the Spectral Norms of the Matrices Connected Integer Numbers Sequence, Math.GM, vol. ED-1, University Science, (2011), 1-4
[6] H. Civciv, R. Turkmen, On the Bounds for the Spectral and Norms of the Khatri-Rao Products of Cauchy-Hankel Matrices, J.I.P.AM, 195, vol. ED-7, (2006), 1-11.
[7] A. Nalli, M. Sen, On the Norms of Circulant Matrices with Generalized Fibonacci Numbers, Selçuk J. Appl. Math, vol. 11, no. 1, (2010), 107–116
[8] S. Solak, B. Mustafa, On the Spectral Norms of Toeplitz Matrices with Fibonacci and Lucas Number, HACET J MATH STAT, Vol 42, (1), (2013), 15-19
[9] S. Solak, B. Mustafa, A Particular Matrix and its Some Properties, Scientific Research and Essays, vol. 8, no. 1, (2013), 1–5
[10] S. Solak, R. Turkmen, D. Bozkurt, Upper Bounds for the Spectral and l_p Norms of Cauchy-Toeplitz and Cauchy-Hankel Matrices, Mathematical & Computational Applications, Vol 9, No.1, (2004), 41-47
[11] F. Zhang, Matrix Theory Basic Results and Techniques, Springer Science+ Business Media, New York, (2011).
Cite This Article
  • APA Style

    Seyyed Hossein Jafari-Petroudi, Behzad Pirouz. (2015). A Particular Matrix, Its Inversion and Some Norms. Applied and Computational Mathematics, 4(2), 47-52. https://doi.org/10.11648/j.acm.20150402.13

    Copy | Download

    ACS Style

    Seyyed Hossein Jafari-Petroudi; Behzad Pirouz. A Particular Matrix, Its Inversion and Some Norms. Appl. Comput. Math. 2015, 4(2), 47-52. doi: 10.11648/j.acm.20150402.13

    Copy | Download

    AMA Style

    Seyyed Hossein Jafari-Petroudi, Behzad Pirouz. A Particular Matrix, Its Inversion and Some Norms. Appl Comput Math. 2015;4(2):47-52. doi: 10.11648/j.acm.20150402.13

    Copy | Download

  • @article{10.11648/j.acm.20150402.13,
      author = {Seyyed Hossein Jafari-Petroudi and Behzad Pirouz},
      title = {A Particular Matrix, Its Inversion and Some Norms},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {2},
      pages = {47-52},
      doi = {10.11648/j.acm.20150402.13},
      url = {https://doi.org/10.11648/j.acm.20150402.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.13},
      abstract = {In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - A Particular Matrix, Its Inversion and Some Norms
    AU  - Seyyed Hossein Jafari-Petroudi
    AU  - Behzad Pirouz
    Y1  - 2015/03/19
    PY  - 2015
    N1  - https://doi.org/10.11648/j.acm.20150402.13
    DO  - 10.11648/j.acm.20150402.13
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 47
    EP  - 52
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20150402.13
    AB  - In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices.
    VL  - 4
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics, Payame Noor University, P. O. Box, 1935-3697, Tehran, Iran

  • Department of Mathematics, Azad University of Karaj, Karaj, Iran

  • Sections