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[1] Zhuang Guifen, Chen Jianlong,. Drazin invertibility for matrices over an arbitrary ring [J]. Journal of Southeast University (English Edition), 2011, 27 (2): 230-232. [doi:10.3969/j.issn.1003-7985.2011.02.025]
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Drazin invertibility for matrices over an arbitrary ring()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
27
Issue:
2011 2
Page:
230-232
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2011-06-30

Info

Title:
Drazin invertibility for matrices over an arbitrary ring
Author(s):
Zhuang Guifen;  Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
ring;  generalized factorization;  Drazin inverse;  group inverse
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2011.02.025
Abstract:
In order to study the Drazin invertibility of a matrix with the generalized factorization over an arbitrary ring, the necessary and sufficient conditions for the existence of the Drazin inverse of a matrix are given by the properties of the generalized factorization. Let T=PAQ be a square matrix with the generalized factorization, then T has Drazin index k if and only if k is the smallest natural number such that Akk is regular and Ukk(Vkk)is invertible if and only if k is the smallest natural number such that Akk is regular and(~overU)kk((~overV)kk)is invertible if and only if k is the smallest natural number such that Akk is regular and(＾overU)kk((＾overV)kk)is invertible. The formulae to compute the Drazin inverse are also obtained. These results generalize recent results obtained for the Drazin inverse of a matrix with a universal factorization.

References:

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Memo

Memo:
Biographies: Zhuang Guifen(1977—), female, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10571026, 10871051), Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006, 200802860024).
Citation: Zhuang Guifen, Chen Jianlong.Drazin invertibility for matrices over an arbitrary ring[J].Journal of Southeast University(English Edition), 2011, 27(2):230-232.[doi:10.3969/j.issn.1003-7985.2011.02.025]
Last Update: 2011-06-20