关于长方矩阵的加权群逆的存在性

本文讨论长方矩阵的加权群逆．分别利用减逆和泛分解,给出了长方矩阵的加权群逆存在的几个充要条件以及加权群逆的计算公式．     

长方对偶矩阵的加权对偶群逆的存在性与表示

本文研究了长方对偶矩阵的加权对偶群逆的存在性与表示问题.利用矩阵的秩和分块表示等给出了长方对偶矩阵的加权对偶群逆存在的若干充分必要条件,并在加权对偶群逆存在的情形下给出了其表达式,推广了对偶群逆的相关结论.通过数值例子说明了加权对偶群逆存在时的计算方法.     

环上长方形矩阵的加权群-Moore-Penrose可逆性（英文）

研究了具有对合?的环上长方形矩阵的W加权群-Moore-Penrose可逆性。给出了环上长方形矩阵的W加权Moore-Penrose逆和W加权群逆的存在性的特性。环上长方形矩阵的W加权群-MoorePenrose逆可以被刻画和计算出来。这推广了具有对合?的环上平方矩阵的群-Moore-Penrose逆的结果。结果也适用于(加法)范畴中的态射.     

广义逆AT，S^（2）的几种秩关系式

利用矩阵A的广义逆AT,S^（2）的Moore-Penrose逆表示式,得到了与广义逆AT,S^（2）相关的几种秩等式和不等式,并由此得到了加权Moore-Pensore逆,Moore-Pensore逆,Drazin逆及群逆的相应结论.     

正则环上矩阵的加权广义逆

定义了正则环上矩阵的加权广义逆,得到其存在的充要条件和表达式,推广了以往文献的相应结果.     

gr－正则环和矩阵环的gr－正则性

本文主要证明了（１）当Ｇ是有限群时，Ｇ－型分次环Ｒ是ｇｒ－正则的当且仅当ＲＧ是正则的当且仅当Ｍ＿Ｇ（Ｒ）是ｇｒ－正则的当且仅当对每个和Ｇ的任意非空子集Ｈ和Ｆ，Ｍ＿（ＨＸＦ）（Ｒ）的每个矩阵都有１－逆。（２）当Ｇ是任意群，Ｇ－型分次环只是反ｇｒ－正则的当且仅当Ｆ是反正则的当且仅当对每个和Ｇ的任意作非空子集Ｈ和Ｋ，ＦＭ＿（Ｈ×Ｆ）（Ｒ）的每个矩阵有２－逆当且仅当ＦＭ＿Ｇ（Ｒ）是ｇｒ－反正则的。     

关于环上矩阵的群逆与Drazin逆

本文给出了环上一类方阵有群逆，｛１，５｝－道的充要条件及其它们的表式，推广了体（域）上关于群逆的Ｃｌｉｎｅ定理．此外还首次得到了矩阵有Ｄｒａｚｉｎ逆的判别准则及其它的表式．     

长方矩阵加权群逆的迭代法

1引 言与引理 最近,文[1]定义了长方矩阵的一种加权群逆:设A∈Cm×n,W∈Cn×m.称满足下列矩阵方程组的矩阵X∈Cm×n为A的加W权群逆:(W1)AWXWA=A, (W2)XWAWX=X, (W3)AWX=XWA通常记A的加W权群逆为A#W.若A#W存在,则它是唯一的.     

Z[3]上无限维矩阵广义逆

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.     

关于单矩阵的广义逆(英文)

本文研究了单矩阵的广义逆,得到了单矩阵有内逆的充分必要条件,进一步讨论了结合环上单矩阵的群逆。     

Generalized Inverses of Matrices over Rings

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.     

交换环上三角矩阵模间的线性保持映射(英文)

本文研究了交换环上三角矩阵模间的线性保持问题.利用矩阵计算技巧和局部化技巧,刻画了上三角矩阵T_n(R)上分别保持立方幂等,{1}逆,{1,2}逆和群逆的所有R模自同构集合中的元素,其中R是交换环.     

About the generalized LM-inverse and the weighted Moore-Penrose inverse

The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential determination of the generalized LM-inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM-inverse and the algorithm for the computation of the weighted Moore-Penrose inverse developed by Wang and Chen (1986) in [23] are equivalent algorithms. Both of the algorithms are implemented in the present paper using the package MATHEMATICA. Several rational test matrices and randomly generated constant matrices are tested and the CPU time is compared and discussed.     

环Z/pkZ上s次幂等矩阵及矩阵的加权广义逆

设R=Z/pkZ是模pk的有限局部环,其中p是素数,k>1,p≠2.本文确定了R上n阶s(s≥3)次幂等矩阵的伪标准形,得到了R上n阶矩阵A的加权{ , }-广义逆矩阵的计数定理.     

Fast solving of weighted pairing least-squares systems

This paper presents a generalization of the “weighted least-squares” (WLS), named “weighted pairing least-squares” (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of speed, accuracy, and numerical stability, is based on a special {1, 2, 3}-inverse, whose computation reduces to a very simple generalization of the usual “Cholesky factorization-backward substitution” method for solving linear systems.     

重模剩余类环的矩阵表示

对模m的剩余类环Zm上的多项式环Zm[x]中的任一n次（n≥1）首一多项式P,给出了重模剩余类环Zm[x]/（P）到Zm上的n阶全矩阵环Mn（Zm）的一类单同态,从而实现了Zm[x]/（P）的矩阵表示.若A为P的友矩阵,则Zm[x]/（P）的矩阵表示为{an-1An-1＋…＋a1A＋a0E｜ai∈Zm,0≤i≤n-1}...     

Generalized inverses of tensors via a general product of tensors

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.     

单位上三角矩阵群的注记(Ⅲ)

设k_(ij)(1≤ij≤n)是给定的正整数,分别记G={ (1 k12a12…k1na1n 0 1…k2na2n…… 0 0…1 )|aij∈Z},R={ (0 k12a12…k1na1n……0 0…k2na2n 0 0…1 )|aij∈Z},本文证明:当G成群且G的上、下中心群列重合时,其相伴Lie环L(G)与Lie环R同构,其中R的Lie积定义为[A,B]=AB-BA.即得到了此时L(G)的矩阵表示.     

范畴中态射集减序的刻划

本文研究了范畴中态射集减序的刻划问题，其主要结果是：（１）证得一般范畴情形减序的十四种刻划；（２）将Ｍｉｔｒａ、Ｂａｋｓａｌａｒｙ等人的利用（１）－逆、（１，２）－逆的包含关系及平行和来刻划复矩阵减序的结果推广到素性预加法范畴与带对合的正性预加法范畴中；（３）给出了１９８０年Ｈａｒｔｗｉｇ关于半群减序刻划的一个反例，因此否定了这个刻画．