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Weighted MP weak group inverse Cover

References

  1. A. Ben-Israel, A Cramer rule for least-norm solutions of consistent linear equations, Linear Algebra Appl. 43 (1982), 223–226.
  2. A. Ben-Israel, T.N.E. Grevile, Generalized inverses, theory and applications, Second edition, Canadian Mathematical Society, Springer, New York, Beflin, Heidelberg, Hong Kong, London, Milan, Paris, Tokyo, 2003.
  3. R. Behera, G. Maharana, J.K. Sahoo, Further results on weighted core-EP inverse of matrices, Results Math 75, 174 (2020), https://doi.org/10.1007/s00025-020-01296-z.
  4. C.Y. Deng, H.K. Du, Representations of the Moore-Penrose inverse of 2 × 2 block operator valued matrices, J. Korean Math. Soc. 46(6) (2009), 1139–1150.
  5. G. Dolinar, B. Kuzma, J. Marovt, B. Ungor, Properties of core-EP order in rings with involution, Front. Math. China 14 (2019), 715–736.
  6. D.E. Ferreyra, F.E. Levis, A.N. Priori, N. Thome, The weak core inverse, Aequat. Math. 95 (2021), 351–373.
  7. D.E. Ferreyra, F.E. Levis, N. Thome, Revisiting the core EP inverse and its extension to rectangular matrices, Quaest. Math. 41(2) (2018), 265–281.
  8. D.E. Ferreyra, V. Orquera, N. Thome, A weak group inverse for rectangular matrices, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), 3727–3740.
  9. Z. Fu, K. Zuo, Y. Chen, Further characterizations of the weak core inverse of matrices and the weak core matrix, AIMS Mathematics, 7(3) (2021), 3630–3647.
  10. Y. Gao, J. Chen, Pseudo core inverses in rings with involution, Comm. Algebra 46(1) (2018), 38–50.
  11. Y. Gao, J. Li, Perturbation bounds of core inverse under the Frobenius norm, Bull. Malays. Math. Sci. Soc. 45 (2022), 2361–2371.
  12. C.W. Groetsch, Generalized inverses of linear operators: representation and approximation, in: Monographs and Textbooks in Pure and Applied Mathematics, Vol. 37, Marcel Dekker, Inc., New York, Basel, 1977.
  13. Y. Ke, L. Wang, J. Chen, The core inverse of a product and 2×2 matrice, Bull. Malays. Math. Sci. Soc. 42 (2019), 51–66.
  14. I.I. Kyrchei, Determinantal representations of the core inverse and its generalizations with applications, Journal of Mathematics 2019 (2019), Article ID 1631979, 13 pages.
  15. I.I. Kyrchei, Weighted quaternion core-EP, DMP, MPD, and CMP inverses and their determinantal representations, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM (2020), 114:198, https://doi.org/10.1007/s13398-020-00930-3.
  16. I.I. Kyrchei, D. Mosić, P.S. Stanimirović, Weighted minimization problems for quaternion matrices, Adv. Appl. Clifford Algebras 31, 48 (2021), https://doi.org/10.1007/s00006-021-01153-4.
  17. N. Liu, H. Wang, The characterizations of WG matrix and its generalized CayleyHamilton theorem, Journal of Mathematics 2021 (2021), Article ID 4952943, 10 pages, https://doi.org/10.1155/2021/4952943.
  18. X. Liu, Y. Yu, J. Zhong, Y. Wei, Integral and limit representations of the outer inverse in Banach space, Linear Multilinear Algebra 60 (2012), 333–347.
  19. H. Ma, P.S. Stanimirović, Characterizations, approximation and perturbations of the core-EP inverse, Appl. Math. Comput. 359 (2019), 404–417.
  20. G. Maess, Projection methods solving rectangular systems of linear equations, J. Comput. Appl. Math. 24 (1988), 107–119.
  21. D. Mosić, Maximal classes of operators determining some weighted generalized inverses, Linear Multilinear Algebra 68(11) (2020), 2201–2220.
  22. D. Mosić, Perturbation of the weighted core-EP inverse, Ann. Funct. Anal. 11 (2020), 75–86.
  23. D. Mosić, Weighted core–EP inverse of an operator between Hilbert spaces, Linear Multilinear Algebra 67(2) (2019), 278–298.
  24. D. Mosić, Weighted core-EP inverse and weighted core-EP pre-orders in a C*-algebra, J. Aust. Math. Soc. 111(1) (2021), 76–110.
  25. D. Mosić, J. Marovt, Weighted weak core inverse of operators, Linear Multilinear Algebra 70(20) (2022), 4991–5013.
  26. D. Mosić, P.S. Stanimirović, Expressions and properties of weak core inverse, Appl. Math. Comput. 415 (2022), 126704.
  27. D. Mosić, P.S. Stanimirović, Representations for the weak group inverse, Appl. Math. Comput. 397 (2021), 125957.
  28. D. Mosić, D. Zhang, Weighted weak group inverse for Hilbert space operators, Front. Math. China 15 (2020), 709–726.
  29. K.M. Prasad, K.S. Mohana, Core-EP inverse, Linear Multilinear Algebra 62(6) (2014), 792–802.
  30. S.M. Robinson, A short proof of Cramer’s rule, Math. Mug. 43 (1970), 94–95.
  31. J.K. Sahoo, R. Behera, P.S. Stanimirović, V.N. Katsikis, H. Ma, Core and core-EP inverses of tensors, Comput. Appl. Math. 39, 9 (2020), doi:10.1007/s40314-019-0983-5.
  32. P.S. Stanimirović, Limit representations of generalized inverses and related methods, Appl. Math. Comput. 103 (1999), 51–68.
  33. K.S. Stojanović, D. Mosić, Weighted MPCEP inverse of an operator between Hilbert spaces, Bull. Iran. Math. Soc. 48 (2022), 53–71.
  34. C. Wang, X. Liu, H. Jin, The MP weak group inverse and its application, Filomat 36(18) (2022), 6085–6102.
  35. H. Wang, Core-EP decomposition and its applications, Linear Algebra Appl. 508 (2016), 289–300.
  36. H. Wang, J. Chen, Weak group inverse, Open Mathematics 16 (2018), 1218–1232.
  37. H. Wang, X. Liu, The weak group matrix, Aequat. Math. 93 (2019), 1261–1273.
  38. [38] Y. Wei, D.S. Djordjević, On integral representation of the generalized inverse AT,S(2) A_{T,S}^{\left( 2 \right)} , Appl. Math. Comput. 142 (2003), 189–194.
  39. H. Yan, H. Wang, K. Zuo, Y. Chen, Further characterizations of the weak group inverse of matrices and the weak group matrix, AIMS Mathematics, 6(9) (2021), 9322–9341.
  40. M. Zhou, J. Chen, Y. Zhou, Weak group inverses in proper *-rings, J. Algebra Appl. 19(12) (2020), 2050238.
  41. M. Zhou, J. Chen, Y. Zhou, N. Thome, Weak group inverses and partial isometries in proper *-rings, Linear Multilinear Algebra (2021), https://doi.org/10.1080/03081087.2021.1884639.
  42. Y. Zhou, J. Chen, Weak core inverses and pseudo core inverses in a ring with involution, Linear Multilinear Algebra (2021), https://doi.org/10.1080/03081087.2021.1971151.
  43. H. Zhu, Q.W. Wang, Weighted pseudo core inverses in rings, Linear Multilinear Algebra 68 (2020), 2434–2447.
DOI: https://doi.org/10.2478/auom-2024-0012 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 221 - 246
Submitted on: Nov 13, 2022
Accepted on: Apr 20, 2023
Published on: May 27, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Dijana Mosić, Janko Marovt, published by Ovidius University of Constanta
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