DOI QR코드

DOI QR Code

CHARACTERIZATIONS AND THE MOORE-PENROSE INVERSE OF HYPERGENERALIZED K-PROJECTORS

  • Tosic, Marina (Faculty of Sciences and Mathematics University of Nis)
  • 투고 : 2012.12.12
  • 발행 : 2014.03.31

초록

We characterize hypergeneralized k-projectors (i.e., $A^k=A^{\dag}$). Also, some representation for the Moore-Penrose inverse of a linear combination of hypergeneralized k-projectors is found and the invertibility for some linear combinations of commuting hypergeneralized k-projectors is considered.

키워드

참고문헌

  1. O. M. Baksalary, Revisitation of generalized and hypergeneralized projectors, Statistical Inference, Econometric Analysis and Matrix Algebra VI (2009), 317-324.
  2. J. K. Baksalary, O. M. Baksalary, and X. Liu, Further properties of generalized and hypergeneralized projectors, Linear Algebra Appl. 389 (2004), 295-303. https://doi.org/10.1016/j.laa.2004.03.013
  3. J. K. Baksalary, O. M. Baksalary, X. Liu, and G. Trenkler, Further results on generalized and hypergeneralized projectors, Linear Algebra Appl. 429 (2008), no. 5-6, 1038-1050. https://doi.org/10.1016/j.laa.2007.03.029
  4. J. Benitez, Moore-Penrose inverses and commuting elements of C*-algebras, J. Math. Anal. Appl. 345 (2008), no. 2, 766-770. https://doi.org/10.1016/j.jmaa.2008.04.062
  5. J. Benitez and N. Thome, Characterizations and linear combinations of k-generalized projectors, Linear Algebra Appl. 410 (2005), 150-159. https://doi.org/10.1016/j.laa.2005.03.007
  6. J. Benitez and N. Thome, {k}-group periodic matrices, SIAM. J. Matrix Anal. Appl. 28 (2006), no. 1, 9-25. https://doi.org/10.1137/S0895479803437384
  7. A. Berman, Nonnegative matrices which are equal to their generalized inverse, Linear Algebra Appl. 9 (1974), 261-265. https://doi.org/10.1016/0024-3795(74)90042-1
  8. S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979.
  9. C. Y. Deng, Q. H. Li, and H. K. Du, Generalized n-idempotents and Hyper-generalized n-idempotents, Northeast. Math. J. 22 (2006), no. 4, 387-394.
  10. T. N. E. Greville, Note on the generalized inverse of a matrix product, SIAM Rev. 8 (1966), 518-521. https://doi.org/10.1137/1008107
  11. J. GroB and G. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997), 463-474. https://doi.org/10.1016/S0024-3795(96)00541-1
  12. R. E. Hartwig and K. Spindelbock, Matrices for which A* and $A{\dagger}$ commute, Linear Multilinear Algebra 14 (1983), no. 3, 241-256. https://doi.org/10.1080/03081088308817561
  13. M. Tosic and D. S. Cvetkovic-Ilic, The invertibility of the difference and the sum of commuting generalized and hypergeneralized projectors, Linear Multilinear Algebra 61 (2013), no. 4, 482-493. https://doi.org/10.1080/03081087.2012.689987
  14. M. Tosic, D. S. Cvetkovic-Ilic, and C. Deng, The Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized projectors, Electron. J. Linear Algebra 22 (2011), 1129-1137.