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1.
设X为一复域C上的Banach空间,设T:X→X为一有界线性算子,其指标为k且R(Tk)闭.记T的Drazin逆为TD.设T=T+δT,则在一定条件下,TD有简明分解式TD=TD(I+δTTD)-1=(I+TDδT)-1TD,从而导出了相对误差‖TD-TD< 相似文献
2.
Let ■ be a pre-additive category. Assume that ψ:X→X is a morphism of (?). In this paper, we give the necessary and sufficient conditions for ψ to have the Drazin inverse by using the von Neumann regular inverse for the ψk, and extend a result by Puystjens and Hartwig from the group inverse to Drazin inverse. 相似文献
3.
We investigate the perturbation bound for the W-weighted Drazin inverse of a rectangular matrix and present two explicit expressions for the W-weighted Drazin inverse under the one-sided condition, which extends the results in Appl. Math. Comput. 2004;149:423–430. 相似文献
4.
关于环上矩阵的群逆与Drazin逆 总被引:4,自引:2,他引:4
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. 相似文献
5.
高璟 《数学的实践与认识》2007,37(7):125-128
利用矩阵A的带W权Drazin逆的一个性质特征,对任意的矩阵A∈Cm×n,W∈Cn×m,建立了带W权的Drazin逆Ad,w的一种新的表示式,给出了具体的算法步骤,并且在文末给出了算例. 相似文献
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本文给出了L-零矩阵的广义Bott-Duffin逆及矩阵的加权Drazin逆的若干性质及表达形式. 相似文献
8.
In this paper,we give further results on the Drazin inverse of tensors via the Einstein product.We give a limit formula for the Drazin inverse of tensors.By using this formula,the representations for the Drazin inverse of several block tensor are obtained.Further,we give the Drazin inverse of the sum of two tensors based on the representation for the Drazin inverse of a block tensor. 相似文献
9.
讨论Banach空间中有界线性算子的Drazin逆的扰动问题.利用Jiu Ding在2003年给出的广义Neumann引理,给出关于Drazin逆的一个新扰动定理,并给出误差估计,推广了文献中相应的扰动结果. 相似文献
10.
The necessary and sufficient conditions for the small norm perturbation of a Drazin invertible operator to be still Drazin invertible and the sufficient conditions for the finite rank perturbation of a Drazin invertible operator to be still Drazin invertible are established. 相似文献
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12.
Several new representations of the W-weighted Drazin inverse are introduced. These representations are expressed in terms of various matrix powers as well as in terms of matrix products involving the Moore–Penrose inverse and the usual matrix inverse. Also, the properties of various generalized inverses which arise from derived representations are investigated. The computational complexity and efficiency of the proposed representations are considered. Representations are tested and compared among themselves in a substantial number of randomly generated test examples. 相似文献
13.
It is known that the existence of the group inverse a
# of a ring element a is equivalent to the invertibility of a
2
a
− + 1 − aa
−, independently of the choice of the von Neumann inverse a
− of a. In this paper, we relate the Drazin index of a to the Drazin index of a
2
a
− + 1 − aa
−. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some
questions and remarks.
相似文献
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AbstractThe representations for the Drazin inverse of anti-triangular matrices are obtained under some conditions. Applying these representations, we give a necessary condition for a class of block matrices to have signed Drazin inverse. 相似文献
17.
该文讨论了两个有界线性算子乘积的Drazin可逆性及其逆序律,分别在P与PQP可交换(即P2QP=PQP2)和Q与QPQ可交换(即Q2PQ=QPQ2)等条件下,采用空间分解的方法得到了PQ的Drazin可逆性及其逆序律(PQ)D=QDPD成立的等价条件. 相似文献
18.
On the Generalized Drazin Inverse and Generalized Resolvent 总被引:11,自引:0,他引:11
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in >C
*-algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, 2 × 2 operator matrices are considered. As corollaries, we get some well-known results. 相似文献
19.
给出了环R上幂等矩阵P,Q满足不同条件:(1)PQP=0;(2)PQP=PQ;(3)PQ=QP;(4)PQP=P时P+aQ的Drazin逆的表达式,推广了一些已有的结论. 相似文献
20.
Israr Ali Khan 《Linear and Multilinear Algebra》2013,61(9):1019-1029
In this article, we investigate the Drazin invertibility for the elements of an arbitrary semiring. We give necessary and sufficient conditions for the existence and expressions of the Drazin inverse of an element in an arbitrary semiring. Moreover, we consider the product paq under some additional necessary conditions for which the Drazin inverse of the product paq exists. 相似文献