The Experts below are selected from a list of 78 Experts worldwide ranked by ideXlab platform
Olga Y. Kushel - One of the best experts on this subject based on the ideXlab platform.
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Matrices with totally positive powers and their generalizations
Operators and Matrices, 2015Co-Authors: Olga Y. KushelAbstract:In this paper, eventually totally positive Matrices (i.e. Matrices all whose powers starting at some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of eventually positive Matrices. We mainly focus on the spectral properties of such Matrices. We also study eventually J-sign-symmetric Matrices and Matrices, whose powers are P -Matrices. Mathematics subject classification (2010): Primary 15A48; Secondary 15A18, 15A75.
Nung-sing Sze - One of the best experts on this subject based on the ideXlab platform.
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Optimization of the spectral radius of nonnegative Matrices
Operators and Matrices, 2007Co-Authors: Michael Neumann, Nung-sing SzeAbstract:In a recent paper by Axtell, Han, Hershkowitz, and the present authors, one of the main questions that was considered was finding n×n doubly stochastic Matrices P and Q which solve the multiplicative extremal spectral radius problems minS∈Ωn ρ(SA) and maxS∈Ωn ρ(SA) , respectively. Here A ∈ Rn,n is an arbitrary, but fixed, n × n nonnegative matrix, ρ(·) is the spectral radius of a matrix, and Ωn is the set of all n × n doubly stochastic Matrices. It was shown there that the solution to both problems is attained at some permutation matrix. In this paper we consider an additive version of these problems, namely, of solving the additive extremal spectral radius problems minS∈Ωn ρ(S + A) and maxS∈Ωn ρ(S + A) . As a by product of, actually, solutions to more general spectral radius optimization problems, we obtain here that the solution to both additive spectral radius optimization problems is, once again, attained at some permutation matrix. One of the more general spectral radius optimization problems that we consider here is that of replacing the constrains that the optimization be done on the doubly stochastic Matrices by the weaker constraint of optimizing just on the n × n column or row stochastic Matrices. Mathematics subject classification (2000): 15A48, 15A18.
Hugo J. Woerdeman - One of the best experts on this subject based on the ideXlab platform.
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Refinements on the interlacing of eigenvalues of certain totally nonnegative Matrices
Operators and Matrices, 2007Co-Authors: Shaun M. Fallat, Hugo J. WoerdemanAbstract:It has long been known that the eigenvalues of a totally positive matrix interlace the eigenvalues of its maximal leading principal submatrix. Motivated by recent questions arising from studying the roots of certain biorthogonal polynomials, we extend the classical strict interlacing fact to other classes of totally nonnegative Matrices. Mathematics subject classification (2000): 15A48, 15A13, 33C45.
Shou-qiang Shen - One of the best experts on this subject based on the ideXlab platform.
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The Spectral Norms of Circulant Matrices Involving (k,h)-Fibonacci and (k,h)-Lucas Numbers 1
International Journal of Contemporary Mathematical Sciences, 2014Co-Authors: Shou-qiang ShenAbstract:This paper is an improving of the work from [6], in which the upper and lower bounds for the spectral norms of the Matrices An = Circ(F (k;h) 0 ;F (k;h) 1 ; ;F (k;h) n 1 ) and Bn = Circ(L (k;h) 0 ;L (k;h) 1 ; ;L (k;h) n 1 ) are established. In this new paper, we compute the spectral norms of these Matrices. Mathematics Subject Classication: 15A45, 15A60
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On the Norms of Toeplitz Matrices Involving k-Fibonacci and k-Lucas Numbers
2012Co-Authors: Shou-qiang ShenAbstract:In this paper, we give upper and lower bounds for the spectral norms of Toeplitz Matrices A =[ Fk,i−j] n=1 and B =[ Lk,i−j] n=1 , where Fk,n and Lk,n are the k-Fibonacci and k-Lucas numbers, then obtain some bounds for the spectral norms of Hadamard and Kronecker products of these Matrices. Mathematics Subject Classification: 15A45, 15A60
Xi Rao - One of the best experts on this subject based on the ideXlab platform.
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Some inequalities for the spectral radius of the Hadamard product of two nonnegative Matrices
Journal of Mathematical Inequalities, 2013Co-Authors: Guanghui Cheng, Xi RaoAbstract:In this paper, we propose some sharper upper bounds for the spectral radius of the Hadamard product of two nonnegative Matrices. The results involve the directed graph of the Hadamard product of associated Matrices. Mathematics subject classification (2010): 15A42, 15A18.