共查询到20条相似文献,搜索用时 46 毫秒
1.
Robert D. Gray 《Semigroup Forum》2014,89(1):135-154
The rank of a finite semigroup is the smallest number of elements required to generate the semigroup. A formula is given for the rank of an arbitrary (not necessarily regular) Rees matrix semigroup over a group. The formula is expressed in terms of the dimensions of the structure matrix, and the relative rank of a certain subset of the structure group obtained from subgroups generated by entries in the structure matrix, which is assumed to be in Graham normal form. This formula is then applied to answer questions about minimal generating sets of certain natural families of transformation semigroups. In particular, the problem of determining the maximum rank of a subsemigroup of the full transformation monoid (and of the symmetric inverse semigroup) is considered. 相似文献
2.
本文针对封闭型保单组,利用历年死亡人数随机向量D,将保单组的未来给付现值随机变量和未来损失现值随机变量表达为某个满秩矩阵和D的乘积,根据D服从多项分布的性质,得到未来损失现值随机向量渐近服从多元正态分布的结果,为分析责任准备金提供了一个新的框架. 相似文献
3.
Naomi Shaked-Monderer 《Linear algebra and its applications》2009,431(12):2407-435
Hanna and Laffey gave an upper bound on the cp-rank of a completely positive matrix, in terms of its rank and the number of zeros in a full rank principal submatrix. This bound, for the case that the matrix is positive, was improved by Barioli and Berman. In this paper a new straightforward proof of both results is given, and the same approach is used to improve Hanna and Laffey’s bound in the case that the matrix has a zero entry. 相似文献
4.
求矩阵广义逆的另一种初等变换方法 总被引:1,自引:0,他引:1
讨论了当矩阵A为满秩矩阵时求其广义逆的一种方法,并将此方法推广,给出当A为非满秩矩阵时求其广义逆的一般方法,同时给出算例.本文推广了文献[1]的结果. 相似文献
5.
The purpose of this paper is to show that any generalized network problem whose matrix does not have full row rank can be transformed into an equivalent pure network problem and to give a constructive method for doing this. 相似文献
6.
本文研究行满秩Hankel矩阵分解为一个真正的(proper)Hankel矩阵与一个退化的(de- generate)Hankel矩阵之拟直和的存在性及唯一性问题. 相似文献
7.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2006,132(2):224-228
The algorithm of ∇V-factorization, suggested earlier for decomposing one- and two-parameter polynomial matrices of full row
rank into a product of two matrices (a regular one, whose spectrum coincides with the finite regular spectrum of the original
matrix, and a matrix of full row rank, whose singular spectrum coincides with the singular spectrum of the original matrix,
whereas the regular spectrum is empty), is extended to the case of q-parameter (q ≥ 1) polynomial matrices. The algorithm
of ∇V-q factorization is described, and its justification and properties for matrices with arbitrary number of parameters
are presented. Applications of the algorithm to computing irreducible factorizations of q-parameter matrices, to determining
a free basis of the null-space of polynomial solutions of a matrix, and to finding matrix divisors corresponding to divisors
of its characteristic polynomial are considered. Bibliogrhaphy: 4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 144–153. 相似文献
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Benoît Collins Piotr ?niady 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(2):139
We study asymptotics of the Itzykson-Zuber integrals in the scaling when one of the matrices has a small rank compared to the full rank. We show that the result is basically the same as in the case when one of the matrices has a fixed rank. In this way we extend the recent results of Guionnet and Maïda who showed that for the fixed rank scaling, the Itzykson-Zuber integral is given in terms of the Voiculescu's R-transform of the full rank matrix. 相似文献
11.
The robustness of regression coefficient
estimator is a hot topic in regression analysis all the while. Since
the response observations are not independent, it is extraordinarily
difficult to study this problem for random effects growth curve
models, especially when the design matrix is non-full of rank. The
paper not only gives the necessary and sufficient conditions under
which the generalized least square estimate is identical to the the
best linear unbiased estimate when error covariance matrix is an
arbitrary positive definite matrix, but also obtains a concise
condition under which the generalized least square estimate is
identical to the maximum likelihood estimate when the design matrix
is full or non-full of rank respectively. In addition, by using of
the obtained results, we get some corollaries for the the
generalized least square estimate be equal to the maximum likelihood
estimate under several common error covariance matrix assumptions.
Illustrative examples for the case that the design matrix is full or
non-full of rank are also given. 相似文献
12.
It is proved that a linear transformation on the vector space of upper triangular matrices that maps the set of matrices of minimal rank 1 into itself, and either has the analogous property with respect to matrices of full minimal rank, or is bijective, is a triangular equivalence, or a flip about the south-west north-east diagonal followed by a triangular equivalence. The result can be regarded as an analogue of Marcus–Moyls theorem in the context of triangular matrices. 相似文献
13.
Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the ra 相似文献
14.
R. Radhakrishnan Askar Choudhury 《International Journal of Mathematical Education in Science & Technology》2013,44(3):434-440
Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating univariate integrals for computing the mean and covariance matrix of a multivariate normal distribution. Moment generating function technique is used for computing the mean and covariances between the elements of a Wishart matrix. In this article, an alternative method that uses matrix differentiation and differentiation of the determinant of a matrix is presented. This method does not involve any integration. 相似文献
15.
We compute the singular rank and the idempotent rank of those subsemigroups of the full transformation semigroup that contain
all singular transformations. 相似文献
16.
The rank of a semigroup is the cardinality of a smallest generating set. In this paper we compute the rank of the endomorphism
monoid of a non-trivial uniform partition of a finite set, that is, the semigroup of those transformations of a finite set
that leave a non-trivial uniform partition invariant. That involves proving that the rank of a wreath product of two symmetric
groups is two and then use the fact that the endomorphism monoid of a partition is isomorphic to a wreath product of two full
transformation semigroups. The calculation of the rank of these semigroups solves an open question. 相似文献
17.
For solving large scale linear least‐squares problem by iteration methods, we introduce an effective probability criterion for selecting the working columns from the coefficient matrix and construct a greedy randomized coordinate descent method. It is proved that this method converges to the unique solution of the linear least‐squares problem when its coefficient matrix is of full rank, with the number of rows being no less than the number of columns. Numerical results show that the greedy randomized coordinate descent method is more efficient than the randomized coordinate descent method. 相似文献
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This paper is concerned primarily with a Monte Carlo investigation into the small sample robustness and power of an aligned rank transformation statistic. The aligned rank transformation statistic (ART) is compared to the classical F-test and to Durbin's (1951) rank test for its ability to detect treatment effects in balanced incomplete block (BIB) designs. 相似文献
20.
The dimension of a faithful realization of a finite abstract regular polytope in
some euclidean space is no smaller than its rank. Similarly, that of a discrete
faithful realization of a regular apeirotope is at least one fewer than the rank.
Realizations which attain the minimum are said to be of full rank. The regular
polytopes and apeirotopes of full rank in two and three dimensions were classified
in an earlier paper. In this paper these polytopes and apeirotopes are classified
in all dimensions. Moreover, it is also shown that there are no chiral polytopes
of full rank. 相似文献