We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the gen...We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.展开更多
In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ha, we show that a ＋ b is Drazin invertible if and only if aaD （a ＋ b） is Drazin invertible, w...In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ha, we show that a ＋ b is Drazin invertible if and only if aaD （a ＋ b） is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of （a ＋ b）D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.展开更多
Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group invers...Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices（ABCD）over a ring with unity 1 under the following conditions respectively： （i） B = C, D = 0,B#and（BπA0#both exist; （ii） B is invertible and m = n;（iii）A#and （D - CA#B）# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.展开更多
基金supported by the Ministry of Education and Science,Republic of Serbia(174007)
文摘We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.
基金Supported by the National Natural Science Foundation of China(11361009)the Guangxi Provincial Natural Science Foundation of China(2013GXNSFAA019008)Science Research Project 2013 of the China-ASEAN Study Center(Guangxi Science Experiment Center)of Guangxi University for Nationalities
文摘In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ha, we show that a ＋ b is Drazin invertible if and only if aaD （a ＋ b） is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of （a ＋ b）D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.
基金Acknowledgements The authors were grateful to the referees for their constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China （Grant No. 11371109） and the Education Department of Heilongjiang Province of China （No. 12541605）.
文摘Abstract We first consider the group inverses of the block matrices（AB0C）over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices（ABCD）over a ring with unity 1 under the following conditions respectively： （i） B = C, D = 0,B#and（BπA0#both exist; （ii） B is invertible and m = n;（iii）A#and （D - CA#B）# both exist, C = CAA#, where A and D are m × m and n × n matrices, respectively.
基金supported by the National Natural Science Foundation of China under grant 10971024the Speeialized Research Fund for the Doetoral Program of Higher Edueation under grant 200802860024the Natural Science Foundation of Jiangsu Province under grant BK2010393
