Search

An n-by-n real symmetric matrix $ H=[h_{i,j}] $ H = [ h i , j ] is said to be a Hankel matrix if $ h_{i,j}=h_{i-1,j+1} $ h i , j = h i − 1 , j + 1 , for each $ i=2,\ldots,n $ i = 2 , ... , n and $ j=1,\ldots,n-1 $ j = 1 , ... , n − 1. The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks when a list $ \Lambda =\{\lambda _{1},\ldots,\lambda _{n}\} $ Λ = { λ 1 , ... , λ n } of real numbers is the spectrum of an n-by-n symmetric nonnegative matrix H. In this paper, we search for conditions on the list $ \Lambda =\{\lambda _{1},\ldots,\lambda _{n}\} $ Λ = { λ 1 , ... , λ n } for the matrix H to be Hankel. For n = 3, sufficient conditions are established. In particular, a necessary and sufficient condition is obtained if Λ is a list of three nonnegative numbers. Also, if $ \sum _{i=1}^{n}\lambda _{i}=0 $ ∑ i = 1 n λ i = 0 , we give conditions for realizability by a Hankel matrix. Finally, we present a special type of list that can serve as the spectrum of a Hankel nonnegative matrix with positive trace. Several of our results are constructive and provide a Hankel realizing matrix. [ABSTRACT FROM AUTHOR]

An n × n matrix C is said to be centrosymmetric if it satisfies the relation JCJ = C, where J is the n × n counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively in the literature. Many results for centrosymmetric matrices have been generalized to wider classes of matrices that arise in a wide variety of disciplines. In this paper, we obtain interesting spectral properties for nonnegative centrosymmetric matrices. We show how to change one single eigenvalue, two or three eigenvalues of an n × n nonnegative centrosymmetric matrix without changing any of the remaining eigenvalues, the nonnegativity, or the centrosymmetric structure. Moreover, our results allow partially answer some known questions given by [Guo W. Eigenvalues of nonnegative matrices. Linear Algebra Appl. 266;1997:261–270] and by [Guo S, Guo W. Perturbing non-real eigenvalues of non-negative real matrices. Linear Algebra Appl. 426;2007:199–203]. Our proofs generate algorithmic procedures that allow one to compute a solution matrix. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper hounds for the distance signless Laplacian spectral radius of G are derived. Some of the above mentioned bounds are sharp and the graphs attaining the corresponding bound are characterized. Several illustrative examples are included. [ABSTRACT FROM AUTHOR]

We give a necessary and sufficient condition for the nonnegative inverse elementary divisors problem to have a solution, in the case of listssatisfyingFor the casewe give new sufficient conditions. Our results improve previous results and generate an algorithmic procedure to compute a solution matrix. [ABSTRACT FROM AUTHOR]

Introduction and Objectives: The aim of this study was to examine the efficiency of the averaging technique for estimating multiple auditory steady state responses in normal hearing subjects and to provide quantifiable stopping criteria at near-threshold intensities., Methods: Multiple amplitude-modulated (89-115 Hz) tones (500, 1,000, 2,000 and 4,000 Hz) were simultaneously presented to both ears at a fixed intensity of 40 dB HL. A total of 128 data epochs were averaged (23.9 minutes)., Results: The results showed that "classic" ensemble averaging, although accurate and time-efficient in most cases, could not extract all near-threshold MSSR from noise, even after recording a considerable number of sweeps. The present study also proposed a different approach to evaluate the background noise based on evaluating the mean of the variance close to the signal., Conclusions: The study proposed quantitative parameters to establish stopping criteria during auditory steady-state recordings., (Copyright © 2010 Elsevier España, S.L. All rights reserved.)