Πεπερασμένοι χώροι Krein και πολυωνυμικοί πίνακες

Ανδρεάδης, Γεώργιος; Andreadis, Georgios

dc.contributor.author	Ανδρεάδης, Γεώργιος	el
dc.contributor.author	Andreadis, Georgios	en
dc.date.accessioned	2020-09-03T08:41:13Z
dc.date.available	2020-09-03T08:41:13Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/51056
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.18754
dc.rights	Default License
dc.subject	Χώροι Krein	el
dc.subject	Πολυωνυμικοί πίνακες	el
dc.subject	Αόριστο εσωτερικό γινόμενο	el
dc.subject	Πίνακες	el
dc.subject	Eσωτερικό γινόμενο	el
dc.title	Πεπερασμένοι χώροι Krein και πολυωνυμικοί πίνακες	el
heal.type	bachelorThesis
heal.classification	Εφαρμοσμένη Ανάλυση	el
heal.classification	Πολυωνυμικοί πίνακες	el
heal.classification	Αόριστο εσωτερικό γινόμενο	el
heal.language	el
heal.access	campus
heal.recordProvider	ntua	el
heal.publicationDate	2020-02-26
heal.abstract	In this thesis, we study Krein spaces and their relation to matrix polynomials. Krein spaces are of very resent origin. This thesis has a lot of references from the phD of P. Zizler who studied linear operators and matrix polynomials in Krein spaces. Krein spaces are inner product spaces with an inde nite inner product, which di er from the known de nite inner product. In the study of in nite dimensional Krein spaces the basic tool is linear operators. In this thesis, we focus on nite dimensional Krein spaces, where we use matrix polynomials instead of linear operators. Initially, in the introductory chapter we present some important properties of the de nite inner product, the induced norm and of Hilbert spaces. Hilbert spaces are complete inner product spaces, and there is a close relation of them and Krein spaces. We, also, introduce the basic elements of matrix polynomials, and we present the Smith form, from which elementary divisors are arised. Then, in the second chapter, we de ne the inde nite inner prooduct, and we introduce Krein spaces and Pontryagin spaces, which are inde nite inner product spaces. In the nite dimensional case, a Krein space is a Pontryagin space. Consequently, in the third chapter, we study matrix polynomials and their relation to di erential equations and some important notions, such as of the sign characteristic and the order of neutrality. Also, there is a special reference to selfadjoint matrix polynomials. Finally, the fourth chapter deals with matrix polynomials of constant signature, and the properties of its order of neutrality.	en
heal.advisorName	Ψαρράκος, Παναγιώτης	el
heal.committeeMemberName	Γιαννακάκης, Νικόλαος	el
heal.committeeMemberName	Καννελόπουλος, Βασίλειος	el
heal.committeeMemberName	Ψαρράκος, Παναγιώτης	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών. Τομέας Μαθηματικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	61 σ.
heal.fullTextAvailability	false