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1.
研究了包含η-厄尔米特矩阵的四元数矩阵方程组.用四元数矩阵的秩和广义逆给出了一个包含η-厄尔米特矩阵的四元数矩阵方程组相容的充分必要条件.进一步地,用四元数矩阵的广义逆给出了这个四元数矩阵方程组的通解表达式.  相似文献   

2.
依据分裂四元数的概念,首先,给出了分裂四元数的实表示矩阵形式,将对分裂四元数的研究转化为实数域上四阶矩阵的研究;其次,根据分裂四元数不同的极表示形式,得到了分裂四元数实表示矩阵相应的棣莫弗定理,推广了欧拉公式,并给出了单位分裂四元数的实表示矩阵方程的求根公式.最后,通过算例验证了结论的正确性.  相似文献   

3.
四元数矩阵的实表示与四元数矩阵方程   总被引:7,自引:0,他引:7  
四元数矩阵与四元数矩阵方程在力学和工程问题的理论研究和实际数值计算中都起到重要的作用.该文借助四元数矩阵的实表示方法,研究了一般四元数矩阵方程AXB-CYD=E的解的问题,给出了一种求解四元数矩阵方程的算法技巧.该文还得到了四元数矩阵的Roth's定理.  相似文献   

4.
本文给出了四元数矩阵惯性的定义,讨论了四元数体上Lyapunov矩阵方程的唯一解,推广了一般惯性定理、Lyapunov稳定性定理、Carlson-Schneider定理、Stein稳定性定理等一些重要的结果到四元数矩阵,同时得出了四元数体上稳定矩阵的一些判别条件.  相似文献   

5.
本文给出了正定四元数矩阵的定义,同时给出了正定四元数矩阵的一个充要条件,一个必要条件,一个充分条件.  相似文献   

6.
郑秉文 《工科数学》1998,14(4):99-101
本文给出了正定四元数矩阵的定义,同时给出了正定四元数矩阵的一个充要条件,一个必要条件,一个充分条件。  相似文献   

7.
彭霞春 《数学理论与应用》2002,22(2):119-121,124
本文给出了四元数矩阵函数的定义,讨论了四元数矩阵函数的一些性质。  相似文献   

8.
四元数体上的矩阵及其优化理论   总被引:9,自引:0,他引:9  
刘建洲 《数学学报》1992,35(6):831-838
本文引入了四元数体 Q 上的广义双随机矩阵,给出了它与优化的关系.由此,我们得出了四元数矩阵奇异值的一些重要不等式,特别是得出了四元数矩阵的和与积的奇异值不等式.我们还讨论了四元数自共轭矩阵的和与积的特征值等.推广了复数域上矩阵的许多著名结果.  相似文献   

9.
本文利用四元数矩阵的奇异值分解给出四元数EP矩阵的一个刻画,并得到四元数EP矩阵减序,左(右)星序,星序的相应刻画定理与性质定理.  相似文献   

10.
四元数矩阵方程AXAH=B的最小二乘解   总被引:8,自引:2,他引:6  
刘永辉 《数学研究》2003,36(2):145-150
引入了四元数矩阵范数的概念,通过使用四无数矩阵的奇异值分解,给出了四元数矩阵方程AXA^H=B在最小二乘意义下的Hermitian解以及Skew-Hermitian解.  相似文献   

11.
The problem of scheduling in permutation flowshops is considered in this paper with the objectives of minimizing the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, with each objective considered separately. Lower bounds on the given objective (corresponding to a node generated in the scheduling tree) are developed by solving an assignment problem. Branch-and-bound algorithms are developed to obtain the best permutation sequence in each case. Our algorithm incorporates a job-based lower bound (integrated with machine-based bounds) with respect to the weighted flowtime/weighted tardiness/weighted flowtime and weighted tardiness, and a machine-based lower bound with respect to the weighted earliness of jobs. The proposed algorithms are evaluated by solving many randomly generated problems of different problem sizes. The results of an extensive computational investigation for various problem sizes are presented. In addition, one of the proposed branch-and-bound algorithms is compared with a related existing branch-and-bound algorithm.  相似文献   

12.
In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities. It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems of generalized vector variational inequalities. The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees for comments and suggestions improving the final draft of this paper.  相似文献   

13.
For one definition of weighted pseudoinversion with singular weights, we establish necessary and sufficient conditions for the existence and uniqueness of a solution of a system of matrix equations. Expansions of weighted pseudoinverse matrices in matrix power series and matrix power products are obtained. A relationship between weighted pseudoinverse matrices the weighted normal pseudosolutions is established. Iterative methods for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions are constructed.  相似文献   

14.
加权极分解   总被引:1,自引:0,他引:1       下载免费PDF全文
In this paper, a new matrix decomposition called the weighted polar decomposition is considered. Two uniqueness theorems of weighted polar decomposition are presented, and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.  相似文献   

15.
岑建苗 《数学杂志》2006,26(1):37-43
本文推广范畴上态射集中的星序理论.引进范畴上态射集中的加权星序.利用态射集的加权广义逆来刻划态射集中的加权星序.给出了态射集中的加权星序和态射的加权广义逆之间的一些关系.得到了态射集中的加权星序的一些刻划和性质.  相似文献   

16.
The spectra of weighted graphs are given attention by some authors because the graphs in the design of networks and electronic circuits are usually weighted. In this short paper, we completely determine the spectra of weighted double stars. We also give the weighted double star that achieves the maximal spectral radius.  相似文献   

17.
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.  相似文献   

18.
The computational methods of the mode attenuation and group,velocity in shallow water are discussed and two novel modified weighted integral formulae are presented. The accuracy of the modified weighted integral formulae, cycle distance formulae and weighted integral formulae in the Pekeris channel is compared theoretically and numerically. Transmission losses are calculated by those three kinds of formulae in a shallow water. Theoretical analyses and numerical results show that the modified weighted integral formulae provide higher accuracy than the weighted integral formulae. So the modified weighted integral formulae can be widely used for computing the shallow water acoustic field. Project supported by the National Natural Science Foundation of China (Grant No. 19574061).  相似文献   

19.
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.  相似文献   

20.
Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are ${(1 - \overline{w}z)^{-\kappa}}$ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces.  相似文献   

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