Left and right W -weighted G -Drazin inverses and new matrix partial orders

• David E. Ferreyra ^[1] ; Dijana Mosić ^[2] ; Albina N. Priori ^[1] ; María Luz Llanes ^[1]
  1. [1] Universidad Nacional de R´ıo Cuarto,Argentina
  2. [2] University of Niˇs, Serbia
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 125-141
• Idioma: inglés
• DOI: 10.33044/revuma.5023
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates a way to define left and right versions of the class of G-Drazin inverses for complex rectangular matrices. More precisely, the concepts of W-weighted left and right G-Drazin inverses are introduced and characterized by means of a simultaneous core-nilpotent decomposition as well as by a certain system of matrix equations. Then new partial orders associated with these weighted generalized inverses are presented and studied.

• Referencias bibliográficas
  • A. Ben-Israel and T. N. E. Greville, Generalized inverses: Theory and applications, second ed., CMS Books Math./Ouvrages Math. SMC 15, Springer,...
  • S. L. Campbell and C. D. Meyer, Generalized inverses of linear transformations, Classics in Applied Mathematics 56, Society for Industrial...
  • R. E. Cline and T. N. E. Greville, A Drazin inverse for rectangular matrices, Linear Algebra Appl. 29 (1980), 53–62. DOI MR Zbl
  • C. Coll, M. Lattanzi, and N. Thome, Weighted G-Drazin inverses and a new pre-order on rectangular matrices, Appl. Math. Comput. 317 (2018),...
  • D. E. Ferreyra, M. Lattanzi, F. E. Levis, and N. Thome, Parameterized solutions X of the system AXA=AEA and AkEAX=XAEAk for matrix...
  • D. E. Ferreyra, M. Lattanzi, F. E. Levis, and N. Thome, Solving an open problem about the G-Drazin partial order, Electron. J. Linear Algebra...
  • A. Hernández, M. Lattanzi, and N. Thome, Weighted binary relations involving the Drazin inverse, Appl. Math. Comput. 253 (2015), 215–223....
  • A. Hernández, M. Lattanzi, and N. Thome, On some new pre-orders defined by weighted Drazin inverses, Appl. Math. Comput. 282 (2016), 108–116....
  • S. K. Mitra, P. Bhimasankaram, and S. B. Malik, Matrix partial orders, shorted operators and applications, Series in Algebra 10, World Scientific,...
  • D. Mosić, Weighted binary relations for operators on Banach spaces, Aequationes Math. 90 no. 4 (2016), 787–798. DOI MR Zbl
  • D. Mosić, Weighted G-Drazin inverse for operators on Banach spaces, Carpathian J. Math. 35 no. 2 (2019), 171–184. DOI MR Zbl
  • D. Mosić, G-outer inverse of Banach spaces operators, J. Math. Anal. Appl. 481 no. 2 (2020), Paper No. 123501. DOI MR Zbl
  • D. Mosić, Solvability to some systems of matrix equations using G-outer inverses, Electron. J. Linear Algebra 36 (2020), 265–276. MR Zbl...
  • D. Mosić and D. S. Djordjević, Weighted pre-orders involving the generalized Drazin inverse, Appl. Math. Comput. 270 (2015), 496–504. DOI...
  • D. Mosić and P. S. Stanimirović, Strong weighted GDMP inverse for operators, Bull. Iranian Math. Soc. 50 no. 3 (2024), Paper No. 43. DOI...
  • D. Mosić and L. Wang, Left and right G-outer inverses, Linear Multilinear Algebra 70 no. 17 (2022), 3319–3344. DOI MR Zbl
  • H. Wang and X. Liu, Partial orders based on core-nilpotent decomposition, Linear Algebra Appl. 488 (2016), 235–248. DOI MR Zbl
  • Y. Wei, Integral representation of the W-weighted Drazin inverse, Appl. Math. Comput. 144 no. 1 (2003), 3–10. DOI MR Zbl