Common properties among various generalized inverses and constrained binary relations

References

• Penrose R. A generalized inverse for matrices. Math Proc Camb Philos Soc. 1955;51:406–413.
   Google Scholar
• Drazin MP. Pseudo-inverses in associative rings and semigroups. Amer Math Monthly. 1958;65:506–514.
   Google Scholar
• Du HK, Deng CY. The representation and characterization of Drazin inverses of operators on a Hilbert space. Linear Algebra Appl. 2005;407:117–124.
   Web of Science ®Google Scholar
• Deng XL, Lin CJ, Deng CY. The structures and properties of some generalized invertible operators. Linear Multilinear Algebra. 2020. DOI:10.1080/03081087.2020.1856029
   Web of Science ®Google Scholar
• Deng CY, Du HK. Representations of the Moore-Penrose inverse for a class of 2-by-2 block operator valued partial matrices. J Korean Math Soc. 2009;46:1139–1150.
   Web of Science ®Google Scholar
• Hartwig RE, Shoaf J. Group inverses and Drazin inverse of bidiagonal and triangular Toeplitz matrices. J Austral Math Soc Ser A. 1977;24:10–34.
   Google Scholar
• Campbell SL, Meyer CD. EP operator and generalized inverses. Canad Math Bull. 1975;18:327–333.
   Web of Science ®Google Scholar
• Baksalary OM, Trenkler G. Core inverse of matrices. Linear Multilinear Algebra. 2010;58:681–697.
   Web of Science ®Google Scholar
• Rakić DS, Dinčić NČ, Djordjević DS. Core inverse and core partial order of Hilbert space operators. Appl Math Comput. 2014;244:283–302.
   Web of Science ®Google Scholar
• Prasad KM, Mohana KS. Core-EP inverse. Linear Multilinear Algebra. 2014;62:792–802.
   Web of Science ®Google Scholar
• Mosić D, Djordjević DS. The gDMP inverse of Hilbert space operators. J Spectr Theory. 2018;8:555–573.
   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
• Yu A, Deng CY. Characterizations of DMP inverse in a Hilbert space. Calcolo. 2016;53:331–341.
   Web of Science ®Google Scholar
• Mehdipour M, Salemi A. On a new generalized inverse of matrices. Linear Multilinear Algebra. 2018;66:1046–1053.
   Web of Science ®Google Scholar
• Mosić D. The CMP inverse for rectangular matrices. Aequationes Math. 2018;92:649–659.
   Web of Science ®Google Scholar
• Xu SX, Chen JL, Mosić D. New characterizations of the CMP inverse of matrices. Linear Multilinear Algebra. 2018;68:790–804.
   Web of Science ®Google Scholar
• Mosić D, Chen JL, Xu SZ. On a new generalized inverse for Hilbert space operator. Quaest Math. 2020;43:1331–1348.
   Web of Science ®Google Scholar
• Wang HX, Chen JL. Weak group inverse. Open Math. 2018;16:1218–1232.
   Web of Science ®Google Scholar
• Mosić D, Zhang DC. Weighted weak group inverse for Hilbert space operators. Front Math China. 2020;15:709–726.
   Web of Science ®Google Scholar
• Zhou MM, Chen JL, Zhou YK. Weak group inverse in proper *-rings. J Algebra Appl. 2020;19(12):Article 2050238.
   PubMed Web of Science ®Google Scholar
• Zhou YK, Chen JL, Zhou MM. m-weak group inverses in a ring with involution. RACSAM Rev R Acad A. 2021;115(2). DOI:10.1007/s13398-020-00932-1
   Google Scholar
• Ferreyra DE, Levis FE, Priori AN, et al. The weak core inverse. Aequationes Math. 2021;95:351–373.
   Web of Science ®Google Scholar
• Zhu HH, Patrício P. Several types of one-sided partial orders in rings. RACSAM Rev R Acad A. 2019;113:3177–3184.
   Google Scholar
• Conway JB. A course in functional analysis. Springer-Verlag, New York; 1990;36–40 .
   Google Scholar
• Wang HX. Core-EP decomposition and its applications. Linear Algebra Appl. 2016;508:289–300.
   Web of Science ®Google Scholar
• Mitra SK. On group inverses and the sharp order. Linear Algebra Appl. 1987;92:17–37.
   Web of Science ®Google Scholar
• Drazin MP. Natural structures on semigroups with involution. Bull Amer Math Soc. 1978;84:139–141.
   Web of Science ®Google Scholar
• Ferreyra DE, Malik SB. Some new results on the core partial order. Linear Multilinear Algebra. 2020. DOI:10.1080/03081087.2020.1841078
   Web of Science ®Google Scholar
• Mitra SK, Bhimasankaram P, Malik SB. Matrix partial orders, shorted operators and applications. New Jersey: World Scientific Publishing Company; 2010.
   Google Scholar
• Wang G, Wei Y, Qiao S. Generalized inverses: theory and computations. Beijing: Science Press; 2003.
   Google Scholar
• Bouldin RH. Generalized inverses and factorizations, recent applications of generalized inverses. Pitman Ser Res Notes Math. 1982;66:233–249.
   Google Scholar
• Nashed MZ, Chen X. Convergence of Newton-like methods for singular operator equations using outer inverses. Numer Math. 1993;66:235–257.
   Web of Science ®Google Scholar
• Wei Y, Zhang N. Condition number related with generalized inverse AT,S(2) and constrained linear systems. J Comput Appl Math. 2003;157:57–72.
   Web of Science ®Google Scholar
• Wei Y, Djordjević DS. On integral representation of the generalized inverse AT,S(2). Appl Math Comput. 2003;142:189–194.
   Web of Science ®Google Scholar
• Wei Y, Wang G. On continuity of the generalized inverse AT,S(2). Appl Math Comput. 2003;136:289–295.
   Web of Science ®Google Scholar
• Wei Y. Generalized inverses of matrices. In: Hogben L, editor. Handbook of linear algebra. 2nd ed. London: Chapman and Hall/CRC; 2014. Chapter 27, 445–469.
   Google Scholar
• Getson AJ, Hsuan FG. [2]-inverse and their statistical applications. Berlin: Springer; 1998. (Lecture notes in statistics; 47).
   Google Scholar
• Husen F, Langenberg P, Getson A. The [2]-inverse with applications to statistics. Linear Algebra Appl. 1985;70:241–248.
   Web of Science ®Google Scholar
• Djordjević DS, Wei Y. Outer generalized inverses in rings. Commun Algebra. 2005;33:3051–3060.
   Web of Science ®Google Scholar
• Drazin MP. A class of outer generalized inverses. Linear Algebra Appl. 2012;436:1909–1923.
   Web of Science ®Google Scholar
• Stanimirović PS, Ćirić M, Stojanović I, et al. Conditions for existence, representations, and computation of matrix generalized inverses. Complexity. 2017;2017:1–27. Article 6429725.
   Google Scholar
• Stanimirović PS, Stojanović I. A class of numerical algorithms for computing outer inverses. J Comput Appl Math. 2014;263:236–245.
   Web of Science ®Google Scholar
• Stanimirović PS, Ćirić M, Lastra A, et al. Representations and symbolic computation of generalized inverses over fields. Appl Math Comput. 2021;406; https://doi.org/10.1016/j.amc.2021.126287.
   Google Scholar
• Deng CY, Yu AQ, Wei Y. Characterizations and representations of the (P,Q)-Outer generalized inverse. Appl Math Comput. 2015;269:432–442.
   Web of Science ®Google Scholar
• Ferreyra DE, Levis FE, Thome N. Revisiting the core-EP inverse and its extension to rectangular matrices. Quaest Math. 2018;41: pp.265–281.
   Web of Science ®Google Scholar
• Ferreyra DE, Levis FE, Thome N. Characterizations of k-commutative equalities for some outer generalized inverses. Linear Multilinear Algebra. 2020;68:177–192.
   Web of Science ®Google Scholar