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991.
Thomas J. Laffey 《Linear algebra and its applications》2007,421(1):97-109
Let σ = (λ1, … , λn) be the spectrum of a nonnegative symmetric matrix A with the Perron eigenvalue λ1, a diagonal entry c and let τ = (μ1, … , μm) be the spectrum of a nonnegative symmetric matrix B with the Perron eigenvalue μ1. We show how to construct a nonnegative symmetric matrix C with the spectrum
(λ1+max{0,μ1-c},λ2,…,λn,μ2,…,μm). 相似文献
992.
A symmetric matrix A is said to be sign-nonsingular if every symmetric matrix with the same sign pattern as A is nonsingular. Hall, Li and Wang showed that the inertia of a sign-nonsingular symmetric matrix is determined uniquely by
its sign pattern. The purpose of this paper is to present an efficient algorithm for computing the inertia of such symmetric
matrices. The algorithm runs in time for a symmetric matrix of order n with m nonzero entries. In addition, it is shown to be NP-complete to decide whether the inertia of a given symmetric matrix is
not determined by its sign pattern. 相似文献
993.
Based on the theory of inverse eigenvalue problem, a correction of an approximate model is discussed, which can be formulated
as NX=XΛ, where X and Λ are given identified modal and eigenvalues matrices, respectively. The solvability conditions for a symmetric skew-Hamiltonian
matrix N are established and an explicit expression of the solutions is derived. For any estimated matrix C of the analytical model, the best approximation matrix to minimize the Frobenius norm of C − N is provided and some numerical results are presented. A perturbation analysis of the solution is also performed, which has scarcely appeared in existing literatures.
Supported by the National Natural Science Foundation of China(10571012, 10771022), the Beijing Natural Science Foundation
(1062005) and the Beijing Educational Committee Foundation (KM200411232006, KM200611232010). 相似文献
994.
We say that two graphs G and H with the same vertex set commute if their adjacency matrices commute. In this article, we show that for any natural number r, the complete multigraph K is decomposable into commuting perfect matchings if and only if n is a 2‐power. Also, it is shown that the complete graph Kn is decomposable into commuting Hamilton cycles if and only if n is a prime number. © 2006 Wiley Periodicals, Inc. J Combin Designs 相似文献
995.
We consider the biorthogonal polynomials associated to the two-matrix model where the eigenvalue distribution has potentials V1,V2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals (hard-edges). We show that these polynomials satisfy certain recurrence relations with a number of terms di depending on the number of hard-edges and on the degree of the rational functions . Using these relations we derive Christoffel–Darboux identities satisfied by the biorthogonal polynomials: this enables us to give explicit formulæ for the differential equation satisfied by di+1 consecutive polynomials, We also define certain integral transforms of the polynomials and use them to formulate a Riemann–Hilbert problem for (di+1)×(di+1) matrices constructed out of the polynomials and these transforms. Moreover, we prove that the Christoffel–Darboux pairing can be interpreted as a pairing between two dual Riemann–Hilbert problems. 相似文献
996.
997.
Wang Zhou 《Transactions of the American Mathematical Society》2007,359(11):5345-5363
Suppose that we have observations from a -dimensional population. We are interested in testing that the variates of the population are independent under the situation where goes to infinity as . A test statistic is chosen to be , where is the sample correlation coefficient between the -th coordinate and the -th coordinate of the population. Under an independent hypothesis, we prove that the asymptotic distribution of is an extreme distribution of type , by using the Chen-Stein Poisson approximation method and the moderate deviations for sample correlation coefficients. As a statistically more relevant result, a limit distribution for , where is Spearman's rank correlation coefficient between the -th coordinate and the -th coordinate of the population, is derived.
998.
Li Ping HUANG 《数学学报(英文版)》2007,23(1):95-102
Let D be any division ring with an involution,Hn (D) be the space of all n × n hermitian matrices over D. Two hermitian matrices A and B are said to be adjacent if rank(A - B) = 1. It is proved that if φ is a bijective map from Hn(D)(n ≥ 2) to itself such that φ preserves the adjacency, then φ^-1 also preserves the adjacency. Moreover, if Hn(D) ≠J3(F2), then φ preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices. 相似文献
999.
本文由有限域上交错矩阵方程XK2υX′=0的解数公式得到q超几何级数2Φ0的一个基本恒等式,并且用它能直接把一些特殊矩阵的这类方程的解数由函数2Φ0表出.另外还用2Φ0的一个恒等式得出Fq上m阶特殊矩阵的个数. 相似文献
1000.
《Journal of Nonlinear Mathematical Physics》2013,20(1):105-116
We identify a solvable dynamical system — interpretable to some extent as a many-body problem — and point out that — for an appropriate assignment of its parameters — it is entirely isochronous, namely all its nonsingular solutions are completely periodic (i.e., periodic in all degrees of freedom) with the same fixed period (independent of the initial data). We then identify its equilibrium configurations and investigate its behavior in their neighborhood. We thereby identify certain matrices — of arbitrary order — whose eigenvalues are all rational numbers: a Diophantine finding. 相似文献