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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 213458, 9 pages
Note on the Invariance Properties of Operator Products Involving Generalized Inverses
1College of Science, Guangxi University for Nationalities, Nanning 530006, China
2School of Mathematical Sciences, Monash University, Melbourne, VIC 3800, Australia
Received 9 July 2013; Accepted 23 December 2013; Published 6 February 2014
Academic Editor: Jaan Janno
Copyright © 2014 Xiaoji Liu et al. 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.
- A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer, New York, 2nd edition, 2003.
- C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, NY, USA, 1971.
- R. Penrose, “A generalized inverse for matrices,” Proceedings of Cambridge Philosophical Society, vol. 51, pp. 406–413, 1955.
- G. Wang, Y. Wei, and S. Qiao, Generalized Inverses: Theory and Computations, Science Press, Beijing, China, 2004.
- J. K. Baksalary and R. Kala, “Range invariance of certain matrix products,” Linear and Multilinear Algebra, vol. 14, no. 1, pp. 89–96, 1983.
- J. K. Baksalary and T. Mathew, “Rank invariance criterion and its application to the unified theory of least squares,” Linear Algebra and Its Applications, vol. 127, pp. 393–401, 1990.
- J. K. Baksalary and T. Pukkila, “A note on invariance of the eigenvalues, singular values, and norms of matrix products involving generalized inverses,” Linear Algebra and Its Applications, vol. 165, pp. 125–130, 1992.
- J. K. Baksalary and O. M. Baksalary, “An invariance property related to the reverse order law,” Linear Algebra and Its Applications, vol. 410, pp. 64–69, 2005.
- J. Groß and Y. Tian, “Invariance properties of a triple matrix product involving generalized inverses,” Linear Algebra and Its Applications, vol. 417, no. 1, pp. 94–107, 2006.
- Z. Xiong and Y. Qin, “Invariance properties of an operator product involving generalized inverses,” Electronic Journal of Linear Algebra, vol. 22, pp. 694–703, 2011.
- D. S. Djordjević and N. Č. Dinčić, “Reverse order law for the Moore-Penrose inverse,” Journal of Mathematical Analysis and Applications, vol. 361, no. 1, pp. 252–261, 2010.