共查询到19条相似文献,搜索用时 187 毫秒
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主要指出文[1]关于M-P广义逆若干定理成立遗漏的条件,并在文[1]的基础上对M-P广义逆进行深入研究,得到关于Quantale矩阵M-P广义逆的一些新结论. 相似文献
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研究整环Z[3]上无限维矩阵V关于无限维矩阵构造下的逆、M-P逆和群逆,给出V的不同的逆、M-P逆等,推广了Saranya和Sivakumar的结果,并且得到Z[3]上无限维矩阵广义逆更广泛的性质. 相似文献
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设R是一个局部环,A是一个可相似对角化的n阶矩阵.利用矩阵方法研究了环R上矩阵A的广义逆半群的子集,得到了其做成正规子群的条件和其中元素可逆的条件,也得到了矩阵广义逆半群的一些性质. 相似文献
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本文给出了利用特征多项式求矩阵广义逆AT,S(2)的一种计算方法,并由此得到了加权M-P逆AM,N+、M-P逆A+、Drazin逆Ad及群逆A9的相应计算方法,推广了文献[2]的结果. 相似文献
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幂等右侧Quantale上的幂零矩阵 总被引:2,自引:0,他引:2
讨论幂等右侧Quantale上的幂零矩阵的若干性质,给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件,得到了幂零矩阵的幂零指数的刻画定理。 相似文献
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广义正定矩阵有一系列推广,研究了一类广义正定矩阵,得到了这类广义正定矩阵的一些性质,并利用这些性质得到了这类广义正定矩阵的一些行列式不等式. 相似文献
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吴炎 《纯粹数学与应用数学》2012,(2):155-166
设R是2为单位的局部环.研究了R上三个两两可换的n阶非零幂等矩阵的线性组合广义逆之间的包含关系,确定了R上一类特殊矩阵广义逆的列表算法.利用这种列表算法和相关的矩阵理论,得到了这些矩阵线性组合广义逆之间的包含关系的充要条件,推广了矩阵自反广义逆的逆反律的相关结果. 相似文献
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该文使用投影算子方法研究任意除环上矩阵的广义逆, 建立了具有指定值域和零空间的{2} 逆的刻划和表示理论. 作为应用, 获得了带有对合函数的Moore Penrose逆, 群逆和Dra zin逆的一些新的表式. 相似文献
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Lizhu SUN Baodong ZHENG Yimin WEI Changjiang BU 《Frontiers of Mathematics in China》2018,13(4):893-911
We define the {i}-inverse (i = 1, 2, 5) and group inverse of tensors based on a general product of tensors. We explore properties of the generalized inverses of tensors on solving tensor equations and computing formulas of block tensors. We use the {1}-inverse of tensors to give the solutions of a multilinear system represented by tensors. The representations for the {1}-inverse and group inverse of some block tensors are established. 相似文献
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An inverse G of a given matrix A which satisfies the property GAG = G is known as a {2}-inverse. This paper presents a three-phase inversion procedure for which the {2}-inverse is a special case. We present the geometry of {2}-inverses and show that, starting from {2}-inverses, various types of generalized inverses can be derived. Two examples of the occurrence of {2}-inverses in statistics are given: one concerning the constrained least-squares estimator, the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi-square distribution. 相似文献
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王松桂 《应用数学学报(英文版)》1996,12(1):22-27
ERKKIP.LISKI(DepertmentofMathematicalSciences,UniversityofTampers,Finland)WANGSONGGUI(王松桂)(DepartmentofAppliedMathematics,Bei... 相似文献
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Yuefeng Gao 《代数通讯》2018,46(1):38-50
Let R be a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse in R. The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary ?-ring case by Raki?, Din?i? and Djordjevi? in 2014. Our definition of pseudo core inverse extends the notion of core inverse to elements of an arbitrary index in R. Meanwhile, it generalizes the notion of core-EP inverse, introduced by Manjunatha Prasad and Mohana for matrices in 2014, to the case of ?-ring. Some equivalent characterizations for elements in R to be pseudo core invertible are given and expressions are presented especially in terms of Drazin inverse and {1,3}-inverse. Then, we investigate the relationship between pseudo core inverse and other generalized inverses. Further, we establish several properties of the pseudo core inverse. Finally, the computations for pseudo core inverses of matrices are exhibited. 相似文献
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In this paper, the traveling wave solutions for a generalized Camassa-Holm equation $u_t-u_{xxt}=\frac{1}{2}(p+1)(p+2)u^pu_x-\frac{1}{2}p(p-1)u^{p-2}u_x^3-2pu^{p-1}u_xu_{xx}-u^pu_{xxx}$ are investigated. By using the bifurcation method of dynamical systems, three major results for this equation are highlighted. First, there are one or two singular straight lines in the two-dimensional system under some different conditions. Second, all the bifurcations of the generalized Camassa-Holm equation are given for $p$ either positive or negative integer. Third, we prove that
the corresponding traveling wave system of this equation possesses peakon, smooth solitary wave solution, kink and anti-kink wave solution, and periodic wave solutions. 相似文献
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Generalized Inverses of Matrices over Rings 总被引:2,自引:0,他引:2
Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved. 相似文献
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在 $T_{1}T_{2}T_{1}=T_{2}$, $T_{2}T_{1}^{k-1}=T_{1}T_{2}^{k-1}$ 和 $T_{1}T_{2}T_{1}=T_{2}T_{1}$的条件下, 得到k-次幂等矩阵线性组合群逆的表示.
另外, 在$T_{1}T_{2}T_{1}=T_{2}$ 和 $T_{1}^{2}T_{2}=T_{2}$ 的条件下, 计算超广义幂等矩阵线性组合Moore-Penrose 广义逆的表示 相似文献