共查询到20条相似文献,搜索用时 15 毫秒
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Bassam Mourad 《Linear and Multilinear Algebra》2013,61(9):1234-1243
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices and doubly stochastic matrices as well as on graph spectra and graph energy. 相似文献
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Mengkun Zhu Niall Emmart Yang Chen Charles Weems 《Mathematical Methods in the Applied Sciences》2019,42(9):3272-3288
We study the asymptotic behavior of the smallest eigenvalue, λN, of the Hankel (or moments) matrix denoted by , with respect to the weight . An asymptotic expression of the polynomials orthogonal with w(x) is established. Using this, we obtain the specific asymptotic formulas of λN in this paper. Applying a parallel numerical algorithm, we get a variety of numerical results of λN corresponding to our theoretical calculations. 相似文献
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The inverse eigenvalue problem of generalized reflexive matrices and its approximation 总被引:1,自引:0,他引:1
This paper studies inverse eigenvalue problems of generalized reflexive matrices and their optimal approximations. Necessary and sufficient conditions for the solvability of the problems are derived, the solutions and their optimal approximations are provided. 相似文献
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M.F. Martínez-Serrano 《Applied mathematics and computation》2009,215(7):2733-2740
In this paper, we give an additive result for the Drazin inverse with its applications, we obtain representations for the Drazin inverse of a 2 × 2 complex block matrix having generalized Schur complement S=D-CADB equal to zero or nonsingular. Several situations are analyzed and recent results are generalized [R.E. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a 2×2 block matrix, SIAM J. Matrix Anal. Appl. 27 (3) (2006) 757-771]. 相似文献
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Bassam Mourad 《Linear and Multilinear Algebra》2004,52(2):99-113
In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented. 相似文献
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Bassam Mourad 《Linear and Multilinear Algebra》2013,61(2):99-113
In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented. 相似文献
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Elizabeth A Sell 《Journal of Number Theory》2004,107(2):266-281
Following the work of Schur and Coleman, we prove the generalized Laguerre polynomial is irreducible over the rationals for all n?1 and has Galois group An if n+1 is an odd square, and Sn otherwise. We also show that for certain negative integer values of α and certain congruence classes of n modulo 8, the splitting field of Ln(α)(x) can be embedded in a double cover. 相似文献
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Tatjana von Rosen 《Linear and Multilinear Algebra》2013,61(5):595-606
In this article, we derive explicit expressions for the entries of the inverse of a patterned matrix that is a sum of Kronecker products. This matrix keeps the Kronecker structure under matrix inversion, and it is used, for example, in statistics, in particular in the linear mixed model analysis. The obtained results present new and extended existing algorithms for the inversion of the considered patterned matrices. We also obtain a closed-form inverse in terms of block matrices. 相似文献
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Tom Wansbeek 《Statistics & probability letters》1985,3(2):95-96
A correlation matrix analyzed by Kotz, Pearn and Wichern (1984) is reanalyzed with known results on balanced ANOVA models. 相似文献
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S. M. Malamud 《Transactions of the American Mathematical Society》2005,357(10):4043-4064
We establish an analog of the Cauchy-Poincare interlacing theorem for normal matrices in terms of majorization, and we provide a solution to the corresponding inverse spectral problem. Using this solution we generalize and extend the Gauss-Lucas theorem and prove the old conjecture of de Bruijn-Springer on the location of the roots of a complex polynomial and its derivative and an analog of Rolle's theorem, conjectured by Schoenberg.
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The left and right inverse eigenvalue problems of generalized reflexive and anti-reflexive matrices 总被引:1,自引:0,他引:1
Let n×n complex matrices R and S be nontrivial generalized reflection matrices, i.e., R∗=R=R−1≠±In, S∗=S=S−1≠±In. A complex matrix A with order n is said to be a generalized reflexive (or anti-reflexive ) matrix, if RAS=A (or RAS=−A). In this paper, the solvability conditions of the left and right inverse eigenvalue problems for generalized reflexive and anti-reflexive matrices are derived, and the general solutions are also given. In addition, the associated approximation solutions in the solution sets of the above problems are provided. The results in present paper extend some recent conclusions. 相似文献
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Recently (see De Vylder & Goovaerts (1984), this issue) so called credibility matrices have been introduced and studied in the framework of general properties of matrices, such as non-negativity, total positivity etc. In the present note we characterize a class of credibility matrices generated by the normed sequence of functions (pl, pl,…, pn) on K = [0, b] where , i=0, …, n, θ ? K, and where ?, g, h are nonnegative (eventually depending on n, n may be finite or infinite). For simplicity we suppose h to be monotonic and continuous. 相似文献
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In this paper, the left and right inverse eigenpairs problem for generalized centrosymmetric matrices is considered. We obtain the necessary and sufficient conditions for the solvability of the problem, and we present the general expression of the solution. The related optimal approximation problem to a given matrix over the solution set is solved. In addition, a numerical algorithm and examples to solve the problem are given. 相似文献
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Until now the concept of a Soules basis matrix of sign patternN consisted of an orthogonal matrix R∈Rn,n, generated in a certain way from a positive n-vector, which has the property that for any diagonal matrix Λ = diag(λ1, … , λn), with λ1 ? ? ? λn ? 0, the symmetric matrix A = RΛRT has nonnegative entries only. In the present paper we introduce the notion of a pair of double Soules basis matrices of sign patternN which is a pair of matrices (P, Q), each in Rn,n, which are not necessarily orthogonal and which are generated in a certain way from two positive vectors, but such that PQT = I and such that for any of the aforementioned diagonal matrices Λ, the matrix A = PΛQT (also) has nonnegative entries only. We investigate the interesting properties which such matrices A have.As a preamble to the above investigation we show that the iterates, , generated in the course of the QR-algorithm when it is applied to A = RΛRT, where R is a Soules basis matrix of sign pattern N, are again symmetric matrices generated by the Soules basis matrices Rk of sign pattern N which are themselves modified as the algorithm progresses.Our work here extends earlier works by Soules and Elsner et al. 相似文献
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In this article we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) power of the complete graph on two vertices. An appealing property of this structure is that all the eigenvalues are distinct. Here we show how to obtain a graph with this property by applying the hierarchical product. In particular, we propose a generalization of the binomial tree and study some of its main properties. 相似文献
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