Uopštenja jezgarne-EP ortogonalnosti i osobine jezgranog-EP pre-uređenja info:eu-repo/semantics/bachelorThesis [9], II, 106 str. 8739886 bytes Mosić, Dijana, 1981- Rakić, Dragan, 1983- Đorđević, Dragan, 1970- srp 2026 The subject of the scientific research in this doctoral dissertationare various generalizations of the concept of core-EP orthogonality,as well as the properties of the core-EP pre-order. The core-EPinverse was first defined for square matrices of an arbitrary index as ageneralization of the core inverse for square matrices of index 1. Thisconcept was subsequently studied for Drazin invertible operators,elements of a ring with involution, and elements of a Banach algebra.The core-EP inverse is applied in solving systems of equations andminimization problems, as well as for defining core-EP orthogonalityand the core-EP pre-order.The aim of this dissertation is, primarily, the generalization of theconcepts of one-sided core orthogonalities and core-EPorthogonality. One-sided core orthogonalities are introduced forsquare matrices of index 1, while this dissertation investigatesorthogonality concepts for Drazin invertible operators of an arbitraryindex. More precisely, left and right core-EP orthogonality and mweakgroup orthogonality are presented, along with their relations toexisting orthogonality concepts. Various characterizations of thesenew orthogonalities are studied. The significance of these newconcepts of orthogonality lies in the study of additivity properties andpre-orders.New properties of the core-EP pre-order are also considered.Specifically, equivalent conditions under which the core-EP pre-orderholds are presented, as well as conditions under which the core-EPorder implies that the reverse order and forward order laws for thecore-EP inverse hold.In a ring with involution, new concepts of orthogonality, whichrepresent generalizations of existing orthogonality concepts foroperators and elements of a ring with involution, are explored.Various properties and characteristics of orthogonal elements areproven, and their matrix forms are also presented. In cases where thenew generalized orthogonalities hold, the corresponding additiveproperties are also studied. Furthermore, the properties of the core-EP pre-order and the reverse order and forward order laws for thecore-EP inverse are investigated.The results of this doctoral dissertation relate to the generalizationsof existing orthogonality concepts to new concepts of orthogonality foroperators and elements of a ring with involution. Existing results aregeneralized and supplemented with new ones. Biografija: str. 105.Bibliografija: str. [98-104]. Datum odbrane: 14.07.2026. Operator theory https://phaidrani.ni.ac.rs/o:3365 cobiss:200217865 thesis:8861 All rights reserved Stanimirović, Olivera, 1986-