A Particular Matrix, Its Inversion and Some Norms

Seyyed Hossein Jafari-Petroudi; Behzad Pirouz

doi:doi:10.11648/j.acm.20150402.13

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A Particular Matrix, Its Inversion and Some Norms

Seyyed Hossein Jafari-Petroudi, Behzad Pirouz

Published in Applied and Computational Mathematics (Volume 4, Issue 2)

Received: 19 February 2015 Accepted: 9 March 2015 Published: 19 March 2015

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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

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[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).

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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

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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

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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

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@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}
}

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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  -

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Author Information

Seyyed Hossein Jafari-Petroudi

Department of Mathematics, Payame Noor University, P. O. Box, 1935-3697, Tehran, Iran
Behzad Pirouz

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

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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

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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