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Journal of Applied Mathematics
Volume 2014, Article ID 918107, 5 pages
http://dx.doi.org/10.1155/2014/918107
Research Article

Weighted Dual Covariance Moore-Penrose Inverses with respect to an Invertible Element in -Algebras

Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

Received 31 May 2014; Accepted 6 July 2014; Published 16 July 2014

Academic Editor: Ferenc Hartung

Copyright © 2014 Hesam Mahzoon. 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.

Linked References

  1. M. H. Alizadeh, “On the covariance of generalized inverses in C*-algebra,” Journal of Numerical Analysis, Industrial and Applied Mathematics, vol. 5, no. 3-4, pp. 135–139, 2011. View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. Mahzoon, “On the covariance of Moore-Penrose inverses in rings with involution,” Abstract and Applied Analysis, vol. 2014, Article ID 309708, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. R. Meenakshi and V. Chinnadurai, “Some remarks on the covariance of the Moore-Penrose inverse,” Houston Journal of Mathematics, vol. 18, no. 2, pp. 167–174, 1992. View at Google Scholar · View at MathSciNet
  4. D. W. Robinson, “On the covariance of the Moore-Penrose inverse,” Linear Algebra and Its Applications, vol. 61, pp. 91–99, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. H. Schwerdtfeger, “On the covariance of the Moore-Penrose inverse,” Linear Algebra and its Applications, vol. 52-53, pp. 629–643, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. D. W. Robinson, “Covariance of Moore-Penrose inverses with respect to an invertible matrix,” Linear Algebra and its Applications, vol. 71, pp. 275–281, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. S. Chipman, “On least squares with insufficient observations,” Journal of the American Statistical Association, vol. 59, no. 308, pp. 1078–1111, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
  8. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, NY, USA, 1971. View at MathSciNet
  9. J. J. Koliha, D. Djordjević, and D. Cvetković, “Moore-Penrose inverse in rings with involution,” Linear Algebra and its Applications, vol. 426, no. 2-3, pp. 371–381, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. R. Harte and M. Mbekhta, “On generalized inverses in C*-algebras,” Studia Mathematica, vol. 103, no. 1, pp. 71–77, 1992. View at Google Scholar · View at MathSciNet
  11. J. J. Koliha, “Continuity and differentiability of the Moore-Penrose inverse in C*-algebras,” Mathematica Scandinavica, vol. 88, no. 1, pp. 154–160, 2001. View at Google Scholar · View at MathSciNet · View at Scopus