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Invertibility of linear combinations of two idempotents   总被引:2,自引:0,他引:2  
Let and be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination is independent of the choice of , if and

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2.
A note on the Drazin inverse of an anti-triangular matrix   总被引:1,自引:0,他引:1  
In this paper we give formulae for the generalized Drazin inverse Md of an anti-triangular matrix M under some conditions. Moreover, some particular cases of these results are also considered.  相似文献
3.
In this paper, we give various characterizations of star order and present some new relationships between the logic order and the star order. We present some necessary and sufficient conditions for which the infimum or upper bound exists with respect to given orders.  相似文献
4.
This note is to present some results on the group invertibility of linear combinations of idempotents when the difference of two idempotents is group invertible.  相似文献
5.
This paper is to present some results on the Drazin invertibility of products and differences of idempotents. In addition, some formulae for the Drazin inverse of sums, differences and products of idempotents are also established.  相似文献
6.
This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.  相似文献
7.
We define and investigate the e-core inverse and f-dual core inverse in a ring with involution as extensions of the core and dual core inverse, respectively. Using these definitions, we present and characterize the e-core partial order and the f-dual core partial order. We describe the sets of all elements a Rickart ∗-ring which are below a given element under the e-core and f-dual core partial order. New characterizations of weighted-EP elements are given too.  相似文献
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