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

Title & Authors
CHARACTERIZATIONS AND THE MOORE-PENROSE INVERSE OF HYPERGENERALIZED K-PROJECTORS
Tosic, Marina;

Abstract
We characterize hypergeneralized k-projectors (i.e., $A^k Keywords hypergeneralized k-projector;linear combination;the Moore-Penrose inverse;nonsingularity; Language English Cited by References 1. O. M. Baksalary, Revisitation of generalized and hypergeneralized projectors, Statistical Inference, Econometric Analysis and Matrix Algebra VI (2009), 317-324. 2. J. K. Baksalary, O. M. Baksalary, and X. Liu, Further properties of generalized and hypergeneralized projectors, Linear Algebra Appl. 389 (2004), 295-303. 3. J. K. Baksalary, O. M. Baksalary, X. Liu, and G. Trenkler, Further results on generalized and hypergeneralized projectors, Linear Algebra Appl. 429 (2008), no. 5-6, 1038-1050. 4. J. Benitez, Moore-Penrose inverses and commuting elements of C*-algebras, J. Math. Anal. Appl. 345 (2008), no. 2, 766-770. 5. J. Benitez and N. Thome, Characterizations and linear combinations of k-generalized projectors, Linear Algebra Appl. 410 (2005), 150-159. 6. J. Benitez and N. Thome, {k}-group periodic matrices, SIAM. J. Matrix Anal. Appl. 28 (2006), no. 1, 9-25. 7. A. Berman, Nonnegative matrices which are equal to their generalized inverse, Linear Algebra Appl. 9 (1974), 261-265. 8. S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979. 9. C. Y. Deng, Q. H. Li, and H. K. Du, Generalized n-idempotents and Hyper-generalized n-idempotents, Northeast. Math. J. 22 (2006), no. 4, 387-394. 10. T. N. E. Greville, Note on the generalized inverse of a matrix product, SIAM Rev. 8 (1966), 518-521. 11. J. GroB and G. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997), 463-474. 12. R. E. Hartwig and K. Spindelbock, Matrices for which A* and$A{\dagger}\$ commute, Linear Multilinear Algebra 14 (1983), no. 3, 241-256.

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