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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 789896, 6 pages
The Group Inverse of the Combinations of Two Idempotent Operators
1School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
2School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Received 1 August 2013; Accepted 7 October 2013
Academic Editor: Jaan Janno
Copyright © 2013 Shunqin Wang and Chunyuan Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Dover Publications, New York, NY, USA, 1991.
- A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley & Sons, New York, NY, USA, 2nd edition, 1980.
- F. A. Graybill, Introduction to Matrices with Applications in Statistics, Wadsworth Publishing Company Inc., Belmont, Calif, USA, 1969.
- D. Buckholtz, “Inverting the difference of Hilbert space projections,” The American Mathematical Monthly, vol. 104, no. 1, pp. 60–61, 1997.
- H. K. Du and Y. Li, “The spectral characterization of generalized projections,” Linear Algebra and Its Applications, vol. 400, pp. 313–318, 2005.
- J. J. Koliha and V. Rakočević, “On the norm of idempotents in -algebras,” The Rocky Mountain Journal of Mathematics, vol. 34, no. 2, pp. 685–697, 2004.
- Y. Li, “The Moore-Penrose inverses of products and differences of projections in a -algebra,” Linear Algebra and Its Applications, vol. 428, no. 4, pp. 1169–1177, 2008.
- J. K. Baksalary and O. M. Baksalary, “Nonsingularity of linear combinations of idempotent matrices,” Linear Algebra and Its Applications, vol. 388, pp. 25–29, 2004.
- J. J. Koliha and V. Rakočević, “The nullity and rank of linear combinations of idempotent matrices,” Linear Algebra and Its Applications, vol. 418, no. 1, pp. 11–14, 2006.
- H. Du, X. Yao, and C. Deng, “Invertibility of linear combinations of two idempotents,” Proceedings of the American Mathematical Society, vol. 134, no. 5, pp. 1451–1457, 2006.
- J. Benítez and N. Thome, “Idempotency of linear combinations of an idempotent matrix and a -potent matrix that commute,” Linear Algebra and Its Applications, vol. 403, pp. 414–418, 2005.
- J. J. Koliha and V. Rakočević, “Invertibility of the difference of idempotents,” Linear and Multilinear Algebra, vol. 51, no. 1, pp. 97–110, 2003.
- J. J. Koliha and V. Rakočević, “Invertibility of the sum of idempotents,” Linear and Multilinear Algebra, vol. 50, no. 4, pp. 285–292, 2002.
- X. Liu, L. Wu, and Y. Yu, “The group inverse of the combinations of two idempotent matrices,” Linear and Multilinear Algebra, vol. 59, no. 1, pp. 101–115, 2011.
- Y. Tian and Y. Takane, “Some properties of projectors associated with the WLSE under a general linear model,” Journal of Multivariate Analysis, vol. 99, no. 6, pp. 1070–1082, 2008.
- Y. Tian and Y. Takane, “On -orthogonal projectors associated with a semi-norm,” Annals of the Institute of Statistical Mathematics, vol. 61, no. 2, pp. 517–530, 2009.
- Y. Tian, “A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications,” Linear and Multilinear Algebra, vol. 59, no. 11, pp. 1237–1246, 2011.
- K. Zuo, “Nonsingularity of the difference and the sum of two idempotent matrices,” Linear Algebra and Its Applications, vol. 433, no. 2, pp. 476–482, 2010.
- C. Bu, M. Li, K. Zhang, and L. Zheng, “Group inverse for the block matrices with an invertible subblock,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 132–139, 2009.
- D. S. Cvetković-Ilić, D. S. Djordjević, and Y. Wei, “Additive results for the generalized Drazin inverse in a Banach algebra,” Linear Algebra and Its Applications, vol. 418, no. 1, pp. 53–61, 2006.
- C. Y. Deng, Q. H. Li, and H. K. Du, “Generalized -idempotents and hyper-generalized -idempotents,” Northeastern Mathematical Journal, vol. 22, no. 4, pp. 387–394, 2006.