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61.
一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质 总被引:3,自引:0,他引:3
本文给出一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质。 相似文献
62.
Jin Bai Kim 《数学研究及应用》1985,5(3):11-13
We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements. 相似文献
63.
Romain Tessera 《Journal of Functional Analysis》2010,259(11):2793-2813
It is known that the algebra of Schur operators on ?2 (namely operators bounded on both ?1 and ?∞) is not inverse-closed. When ?2=?2(X) where X is a metric space, one can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra Aω(X) for a strictly polynomial weight ω is inverse-closed. In this paper, we prove a sharp result on left-invertibility of the these operators. Namely, if an operator A∈Aω(X) satisfies ‖Afp‖?‖fp‖, for some 1?p?∞, then it admits a left-inverse in Aω(X). The main difficulty here is to obtain the above inequality in ?2. The author was both motivated and inspired by a previous work of Aldroubi, Baskarov and Krishtal (2008) [1], where similar results were obtained through different methods for X=Zd, under additional conditions on the decay. 相似文献
64.
Compound matrices are encountered in many fields such as Matrix Theory, Systems Theory, Control Theory, etc. In the present
paper we develop an efficient algorithm computing the Smith normal form of compound matrices. This algorithm is based on a
new theorem establishing an equivalence relation between the Smith normal form of the compounds of a given matrix and the
compounds of the Smith normal form of the given matrix.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
65.
Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data. 相似文献
66.
We investigate the parameter dynamics of eigenvalues of Hamiltonians (‘level dynamics’) defined on symmetric spaces relevant to condensed matter and particle physics. In particular we: (1) identify the appropriate reduced manifold on which the motion takes place, (2) identify the correct Poisson structure ensuring the Hamiltonian character of the reduced dynamics, (3) determine the canonical measure on the reduced space, (4) calculate the resulting eigenvalue density. 相似文献
67.
68.
S. Al-Homidan 《Journal of Optimization Theory and Applications》2007,135(3):583-598
Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the
problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead
of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain
exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an
inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned
conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm. 相似文献
69.
首先将常用类型的模糊矩阵都纳入到了二阶占优模糊矩阵的统一框架之内,然后利用模糊矩阵的有向伴随图,指出了强连通布尔矩阵振荡的一个充要条件,依次证明了强连通的二阶占优布尔矩阵的振荡指数为2n-2,非强连通的二阶占优布尔矩阵的振荡指数为3n-4. 相似文献
70.
For matrices whose eigenvalues are real (such as Hermitian or real symmetric matrices), we derive simple explicit estimates for the maximal (λmax) and the minimal (λmin) eigenvalues in terms of determinants of order less than 3. For 3 × 3 matrices, we derive sharper estimates, which use det A but do not require to solve cubic equations. 相似文献