A Particular Matrix, Its Inversion and Some Norms
Applied and Computational Mathematics
Volume 4, Issue 2, April 2015, Pages: 47-52
Received: Feb. 19, 2015; Accepted: Mar. 9, 2015; Published: Mar. 19, 2015
Views 3117      Downloads 228
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
Article Tools
Follow on us
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.
Positive Definite Matrix, Spectral Norm, Hadamard Inverse, Determinant, Block Diagonal
To cite this article
Seyyed Hossein Jafari-Petroudi, Behzad Pirouz, A Particular Matrix, Its Inversion and Some Norms, Applied and Computational Mathematics. Vol. 4, No. 2, 2015, pp. 47-52. doi: 10.11648/j.acm.20150402.13
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
M. Akbulak, A. Ipek, Hadamard Exponential Hankel Matrix, Its Eigenvalues and Some Norms, Math. Sci. Lett., Vol 1, No. 1, (2012), 81-87
D. Bozkurt, On the l_p Norms of Almost Cauchy-Toeplitz Matrices, Tr. J. of Mathematics, 20, (1996), 545-552
D. Bozkurt, S. Solak, A Note on Bound for Norms of Cuachy-Hankel Matrices, Numerical Linear Algebra, vol. ED-10, (2003), 377-382
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
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.
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
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
S. Solak, B. Mustafa, A Particular Matrix and its Some Properties, Scientific Research and Essays, vol. 8, no. 1, (2013), 1–5
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
F. Zhang, Matrix Theory Basic Results and Techniques, Springer Science+ Business Media, New York, (2011).
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186