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
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Authors
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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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.
Keywords
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
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