Representations of the weighted WG inverse and a rank equation's solution

References

• Baksalary OM, Trenkler G, Core inverse of matrices. Linear Multilinear Algebra. 2010;58(6):681–697.
   Web of Science ®Google Scholar
• Malik SB, Thome N. On a new generalized inverse for matrices of an arbitrary index. Appl Math Comput. 2014;226:575–580.
   Web of Science ®Google Scholar
• Manjunatha Prasad K, Mohana KS. Core EP inverse. Linear Multilinear Algebra. 2014;62(3):792–802.
   Google Scholar
• Wang H, Chen J. Weak group inverse. Open Math. 2018;16:1218–1232.
   Web of Science ®Google Scholar
• Ben-Israel A, Greville TNE. Generalized inverses: theory and applications. 2nd ed. New York: Springer; 2003.
   Google Scholar
• Kirkland SJ, Neumann M. Group inverses of M-matrices and their applications. London: Chapman and Hall/CRC; 2013.
   Google Scholar
• Soleimani F, Stanimirović PS, Soleymani F. Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms. 2015;8:982–998.
   Google Scholar
• Doty KL, Melchiorri C, Bonivento C. A theory of generalized inverses applied to robotics. Int J Rob Res. 1993;12:1–19.
   Web of Science ®Google Scholar
• Xiao GZ, Shen BZ, Wu CK, et al. Some spectral techniques in coding theory. Discrete Math. 1991;87:181–186.
   Web of Science ®Google Scholar
• Cline RE, Greville TNE. A Drazin inverse for rectangular matrices. Linear Algebra Appl. 1980;29:53–62.
   Web of Science ®Google Scholar
• Gao Y. Representations and properties of the W-weighted core-EP inverse. Linear Multilinear Algebra. 2020;68(6):1160–1174.
   Web of Science ®Google Scholar
• Wei Y. A characterization for the W-weighted Drazin inverse and a crammer rule for the W-weighted Drazin inverse solution. Appl Math Comput. 2002;125:303–310.
   Web of Science ®Google Scholar
• Wei Y. Integral representation of the W-weighted Drazin inverse. Appl Math Comput. 2003;144:3–10.
   Web of Science ®Google Scholar
• Kyrchei I. Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. Appl Math Comput. 2015;264:453–465.
   Web of Science ®Google Scholar
• Stanimirović PS, Katsikis VN, Ma H. Representations and properties of the W-weighted Drazin inverse. Linear Multilinear Algebra. 2017;65(6):1080–1096.
   Web of Science ®Google Scholar
• Wang X, Ma H, Stanimirović PS. Recurrent neural network for computing the W-weighted Drazin inverse. Appl Math Comput. 2017;300:1–20.
   Web of Science ®Google Scholar
• Hernández A, Lattanzi M, Thome N. On some new pre-orders defined by weighted Drazin inverses. Appl Math Comput. 2015;282:108–116.
   Web of Science ®Google Scholar
• Hernández A, Lattanzi M, Thome N. Weighted binary relations involving the Drazin inverse. Appl Math Comput. 2015;253:215–223.
   Web of Science ®Google Scholar
• Ferreyra DE, Levis FE, Thome N. Revisiting of the core EP inverse and its extension to rectangular matrices. Quaest Math. 2018;41:265–281.
   Web of Science ®Google Scholar
• Meng LS. The DMP inverse for rectangular matrices. Filomat. 2017;31(19):6015–6019.
   Web of Science ®Google Scholar
• Mosić D. The CMP inverse for rectangular matrices. Aequaetiones Math. 2018;92:649–659.
   Web of Science ®Google Scholar
• Mosić D, Kolundzija MZ. Weighted CMP inverse of an operator between Hilbert spaces. Rev R Acad Cienc Exactas Fis Nat Ser A Math. 2019;113:2155–2173.
   Web of Science ®Google Scholar
• Ferreyra DE. A weak group inverse for rectangular matrices. Rev R Acad Cienc Exactas Fis Nat Ser A Math. 2019;113:3727–3740.
   Web of Science ®Google Scholar
• Chen JL, Zhu HH, Patrício P, et al. Characterizations and representations of core and dual core inverses. Canadian Mathemathics Bulletin. 2017;60(2):269–282.
   Web of Science ®Google Scholar
• Zhou M, Chen J, Stanimirovic PS, et al. Complex varying-parameter Zhang neural networks for computing core and core-EP inverse. Neural Processing Letters. 2020;51(2):1299–1329.
   Web of Science ®Google Scholar
• Wang H. Core-EP decomposition and its applications. Linear Algebra Appl. 2016;508:289–300.
   Web of Science ®Google Scholar
• Ferreyra DE, Levis FE, Thome N. Maximal classes of matrices determining generalized inverses. Appl Math Comput. 2018;333:42–52.
   Web of Science ®Google Scholar
• Wei Y. A characterization and representation of the Drazin inverse. SIAM J Matrix Anal Appl. 1996;17(4):744–747.
   Web of Science ®Google Scholar
• Cvetković-Ilić D. On a problem of Thome and Wei. Appl Math Comput. 2005;166(1):233–236.
   Web of Science ®Google Scholar
• Thome N. Wei Y. Generalized inverses and a block-rank equation. Appl Math Comput. 2003;141:471–476.
   Web of Science ®Google Scholar
• Cline RE. Inverses of rank invariant powers of a matrix. SIAM J Numer Anal. 1968;5:182–197.
   Web of Science ®Google Scholar