态射和的Drazin逆

Abstract

Abstract:

Let C be an additive category. Suppose that φ and η: X→ X are two morphisms of C. If φ and η have the Drazin inverses such that φη=0, then φ+η has the Drazin inverse. If φ has the Drazin inverse φ^D such that 1_X+φ^Dη is invertible. We study the Drazin inverse (resp. group inverse) of f =φ+η and give the necessary and sufficient condition for f^D(resp. f ^#}=(1_X+φ^Dη)^-1φ^D. Finally, we extend the Huylebrouck's result from the group inverse to the Drazin inverse.

Key words: Drazin inverse, Group inverse, Morphism

CLC Number:

15A09

Cite this article

CHEN Jian-Long, PENG Gui-Fen, WEI Yi-Min. The Drazin Inverse of a Sum of Morphisms[J].Acta mathematica scientia,Series A, 2009, 29(3): 538-552.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2009/V29/I3/538

Trendmd

References

[1] Ben-Israel A, Greville T N E. Generalized Inverse: Theory and Applications. New York: Springer, 2003

[2] Gon'zalez N Castro, Koliha J J, Straskraba I. Perturbation on the Drazin inverse. Soochow J Math, 2001, 27: 201--211

[3] Gon\'{z}alez N Castro, Koliha J J, Wei Y M. Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero. Linear Algebra Appl, 2000, 312: 181--189

[4] Hartwig R E, Wang G R, Wei Y M. Some additive results on Drazin inverse. Linear Algebra Appl, 2001, 322: 207--217

[5] Huylebrouck D. The generalized inverse of a sum with radical element: applications. Linear Algebra Appl, 1996, 246: 159--175

[6] Huylebrouck D, Puystjens R. Generalized inverses of a sum with a radical element. Linear Algebra Appl, 1986, 84: 289--300

[7] Wei Y M, Wang G R. The perturbation theory for the Drazin inverse and its applications. Linear Algebra Appl, 1997, 258: 179--186

[8] Wei Y M. Perturbations bound of the Drazin inverse. Appl Math Comput, 2002, 125: 231--244

[9] You H, Chen J L. Generalized inverses of a sum of morphisms. Linear Algebra Appl, 2001, 338: 261--273

[10 }You H, Chen J L. The Drazin inverse of a morphism in additive category. J Math (Wuhan, in Chinese), 2002, 22: 359--364

Related Articles 15

[1]	HAI Jin-Ke, LI Zheng-Xing. ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS [J]. Acta mathematica scientia,Series A, 2014, 34(3): 790-796.
[2]	CHENG Li-Hua, LIAN Tie-Yan. Stability of Cubic Functional Equations in Banach Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(2): 266-273.
[3]	FU Xi. Algebraic Convergence of Negatively Curved Groups [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1142-1147.
[4]	WANG Song. Automorphism Groups of Rank One Lattice Vertex Operator Superalgebras [J]. Acta mathematica scientia,Series A, 2012, 32(2): 290-296.
[5]	LI Zheng-Xing, HAI Jin-Ke. Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class [J]. Acta mathematica scientia,Series A, 2012, 32(2): 344-348.
[6]	ZHANG Yun, CHEN Dong-Jun, XIE Yong-Sheng . Representation of Bounded Linear Operators with Equal Spectral Projections at Zero [J]. Acta mathematica scientia,Series A, 2011, 31(3): 729-736.
[7]	LAI Jia-Jun, XU Yang, QIN Ke-Yun. The Properties of Normed Lattice H Implication Algebras [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1465-1473.
[8]	QI Xiao-Fei, DU Quan-Ping, HOU Jin-Chuan. Additive Maps Satisfying [Φ(A²), Φ(A)] = 0 on the Space of Self-adjoint Operators [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1686-1692.
[9]	ZHONG Jin, LIU Xiao-Ji. The Characterization and Representation of the W-weighted Drazin Inverse of Operators on Hilbert Space [J]. Acta mathematica scientia,Series A, 2010, 30(4): 915-921.
[10]	ZHOU Yong-Dao, LIU Yao-Mei. Minimum Moment Aberration Majorization in Non-isomorphic Asymmetrical Saturated Designs [J]. Acta mathematica scientia,Series A, 2009, 29(5): 1145-1152.
[11]	LIU Xiao-Ji, ZHANG Shi-Guang. The w-weighted Drazin Inverse of Morphisms with Kernels [J]. Acta mathematica scientia,Series A, 2009, 29(3): 741-750.
[12]	Chen Lili; Li Fang. Dual Hopf Algebras from a Quiver and Dual Quiver Quantum Groups [J]. Acta mathematica scientia,Series A, 2009, 29(2): 505-516.
[13]	Zheng Zhaojuan. Automorphism Group, Central Extension and Derivations for a Lie Algebra over Quantum Torus [J]. Acta mathematica scientia,Series A, 2008, 28(6): 1206-1217.
[14]	Pan Yuxia\|Zhang Qingcheng. The Uniqueness of the Decomposition of Lie Supertriple Systems [J]. Acta mathematica scientia,Series A, 2008, 28(6): 1058-1066.
[15]	Su Hong; Zhao Zhenhua; Qiu Dunyuan. On Some p⁶-Groups with p-Groups as Automorphism Groups [J]. Acta mathematica scientia,Series A, 2008, 28(5): 937-941.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Zhou Zongfu; Li Lei; Wang Jinfong; Hu Xiulin. Periodic Solutions for a Class of Degenerate Neutral[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1025 .
[2]	CHENG Mei-Fang, ZHANG Zhen-Qiu. Hypersingular Integrals along Hypersurface on Modulation Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(4): 959 -967 .
[3]	Zhang Liang; Song Weidong. Totally Real Pseudo-umbilical Submanifolds with Flat Normal Bundle of Complex Projective Space [J]. Acta mathematica scientia,Series A, 2007, 27(4): 688 -695 .
[4]	Chu Yuming;Huang Manzi. A Necessary and Sufficient Condition for Quasiconformal Mappings[J]. Acta mathematica scientia,Series A, 2007, 27(5): 949 -954 .
[5]	Gan Shixin; Chen Pingyan. Strong Stability of Pairwise NQD Random Variable Sequences[J]. Acta mathematica scientia,Series A, 2008, 28(4): 612 -618 .
[6]	WANG Mao-Fa, LIU Pei-De. Spectra of Compact Weighted Composition Operators on Dirichlet Type Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(4): 873 -883 .
[7]	XU Yu-Mei. Initial Problems for Nonlinear Second Order Impulsive Integro differential Equation in Banach Space[J]. Acta mathematica scientia,Series A, 2005, 25(1): 47 -56 .
[8]	WANG Kai. Existence of Periodic Solutions for a Type of High Order Neutral Functional Differential Equations[J]. Acta mathematica scientia,Series A, 2009, 29(3): 794 -799 .
[9]	JIANG Yun-Feng, LIU Zong-Ze, LIU Xi-Bei. Commuting Involutions Fixing Isolated Points[J]. Acta mathematica scientia,Series A, 2004, 24(1): 38 -44 .
[10]	LIU Yong-Hui, SHU Chao, CHEN Guan-Liang. Generalized Inverses of Matrices on an Arbitrary Division Ring[J]. Acta mathematica scientia,Series A, 2005, 25(6): 770 -776 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

The Drazin Inverse of a Sum of Morphisms

PDF (PC)