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 ...