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G-Drazin inverse combined with inner inverse (2402.09699v1)

Published 15 Feb 2024 in math.NA and cs.NA

Abstract: This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition. Further, we introduce a binary relation for GD1 inverse and 1GD inverse, along with a few derived properties.

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References (34)
  1. O. M. Baksalary and G. Trenkler. Core inverse of matrices. Linear Multilinear Algebra, 58(5-6):681–697, 2010.
  2. Generalized inverses of linear transformations, volume 56 of Classics in Applied Mathematics. SIAM, Philadelphia, PA, 2009.
  3. S. L. Campbell and C. D. Meyer, Jr. Weak Drazin inverses. Linear Algebra Appl., 20(2):167–178, 1978.
  4. Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAM J. Appl. Math., 31(3):411–425, 1976.
  5. S. Caradus. Generalized inverses and operator theory, queen’s papers in pure and appl. Math., Queen’s Univ., Kingston, 1978.
  6. R. E. Cline and T. Greville. A Drazin inverse for rectangular matrices. Linear Algebra and its Applications, 29:53–62, 1980.
  7. Weighted G-Drazin inverses and a new pre-order on rectangular matrices. Appl. Math. Comput., 317:12–24, 2018.
  8. M. P. Drazin. Pseudo-inverses in associative rings and semigroups. Amer. Math. Monthly, 65:506–514, 1958.
  9. M. P. Drazin. A class of outer generalized inverses. Linear Algebra Appl., 436(7):1909–1923, 2012.
  10. M. P. Drazin. Left and right generalized inverses. Linear Algebra Appl., 510:64–78, 2016.
  11. D. Ferreyra and S. B. Malik. Some new results on the core partial order. Linear and Multilinear Algebra, pages 1–17, 2020.
  12. T. N. Greville and A. Ben-Israel. Generalized inverses: theory and applications. Wiley New York, 1974.
  13. R. E. Hartwig. Schur’s theorem and the Drazin inverse. Pacific J. Math., 78(1):133–138, 1978.
  14. On a partial order defined by the weighted Moore-Penrose inverse. Appl. Math. Comput., 219(14):7310–7318, 2013.
  15. From projectors to 1MP and MP1 generalized inverses and their induced partial orders. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 115(3):Paper No. 148, 13, 2021.
  16. GDMP-inverses of a matrix and their duals. Linear Multilinear Algebra, 2022.
  17. On 2MP-, MP2-and C2MP-inverses for rectangular matrices. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 116(4):Paper No. 156, 2022.
  18. C. F. King. A note on Drazin inverses. Pacific J. Math., 70(2):383–390, 1977.
  19. D. C. Lay. Spectral properties of generalized inverses of linear operators. SIAM Journal on Applied Mathematics, 29(1):103–109, 1975.
  20. H. Ma. Characterizations and representations for the CMP inverse and its application. Linear and Multilinear Algebra, pages 1–16, 2021.
  21. Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications. Appl. Math. Comput., 378:125196, 18, 2020.
  22. S. B. Malik and N. Thome. On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput., 226:575–580, 2014.
  23. K. Manjunatha Prasad and K. S. Mohana. Core-EP inverse. Linear Multilinear Algebra, 62(6):792–802, 2014.
  24. M. Mehdipour and A. Salemi. On a new generalized inverse of matrices. Linear Multilinear Algebra, 66(5):1046–1053, 2018.
  25. L. Meng. The DMP inverse for rectangular matrices. Filomat, 31(19):6015–6019, 2017.
  26. Matrix partial orders, shorted operators and applications, volume 10 of Series in Algebra. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010.
  27. D. Mosić. Weighted gDMP inverse of operators between Hilbert spaces. Bull. Korean Math. Soc., 55(4):1263–1271, 2018.
  28. D. Mosić. Weighted G-Drazin inverse for operators on Banach spaces. Carpathian J. Math., 35(2):171–184, 2019.
  29. D. Mosić and D. S. Djordjević. The gDMP inverse of Hilbert space operators. J. Spectr. Theory, 8(2):555–573, 2018.
  30. The Drazin inverse for singular evolution equations and partial differential operators. In Recent trends in differential equations, volume 1 of World Sci. Ser. Appl. Anal., pages 441–456. World Sci. Publ., River Edge, NJ, 1992.
  31. 1D inverse and D1 inverse of square matrices. To appear in Miskolc Math. Notes.
  32. M. Sheibani Abdolyousefi. The representations of the G-Drazin inverse in a Banach algebra. Hacet. J. Math. Stat., 50(3):659–667, 2021.
  33. The Drazin inverse in multibody system dynamics. Numer. Math., 64(4):521–539, 1993.
  34. H. Wang and X. Liu. Partial orders based on core-nilpotent decomposition. Linear Algebra Appl., 488:235–248, 2016.

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