Uopšteni inverzi i kvazihiponormalne matrice u prostorima sa nedefinisanim skalarnim proizvodom

Abstract

In this dissertation the original results in matrix theory and general inverses theory in finite-dimensional indefinite inner product spaces are presented. Linear relations are used for the extension of some results in degenerate case. In the first part a generalization of the notion of normality and hyponormality is established.Quasihyponormal and strongly quasihyponormal matrices and linear relations are defined in nondegenerate and degenerate indefinite inner product spaces. A characterization of quasihyponormal and strongly quasihyponormal matrices in those spaces is given. In the second part a Moore-Penrose inverse of matrices and linear relations in degenerate indefinite inner product spaces is defined. Some properties of this inverse for matrices in degenerate case are shown. Results in the third part concerns EP matrices in indefinite inner product spaces with respect to indefinite matrix product. These matrices are J-EP matrices. The connection among EP, J-EP matrices and the reverse order law for the Moore- Penrose inverse of the indefinite matrix product is studied.