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master's thesis
Generalizirani inverzi
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:574920
Zibar, Anamarija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Zibar, A. (2018). Generalizirani inverzi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:574920

Zibar, Anamarija. "Generalizirani inverzi." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:574920

Zibar, Anamarija. "Generalizirani inverzi." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:574920

Zibar, A. (2018). 'Generalizirani inverzi', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:574920

Zibar A. Generalizirani inverzi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:574920

A. Zibar, "Generalizirani inverzi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:574920

Metadata
TitleGeneralizirani inverzi
AuthorAnamarija Zibar
MentorSanja Singer (mentor)
Committee memberSanja Singer (predsjednik povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema diplomskog rada je pojam generaliziranog inverza matrice. Prvo poglavlje se bavi Moore--Penroseovim inverzom i njegovom ulogom u rješavanju sustava linearnih jednadžbi. Nadalje, promotrili smo i \(\{i, j, k\}\)-inverze koji zadovoljavaju samo neke od Penroseovih uvjeta, svojstva koja zadovoljavaju i njihovu primjenu. Pokazane su i dvije metode za njegovo računanje, jedna koja se bazira na particioniranju matrice po stupcima i druga koja se bazira na dekompoziciji singularnih vrijednosti matrice. U drugom poglavlju smo promotrili Drazinov inverz i njegov specijalan slučaj, grupni inverz. Spomenute su primjene u teoriji Markovljevih lanaca i u sustavima diferencijalnih jednadžbi. Detaljnije su proučena tri algoritma za njegovo računanje i njihova konvergencija, te njihovo ponašanje na odabranim primjerima.
Abstract (english)
This thesis’ emphasis has been on the theory and application of generalized inverses. The first part is about the Moore–Penrose inverse and its role in finding solutions of linear systems. \(\{i, j, k\}\)-inverse satisfies some, but not all, of the Penrose equations. Its properties and applications are studied. Two methods of computing the Moore–Penrose inverse are mentioned, one relying on partitioning the matrix by columns, and the other on the singular value decomposition. The second part was about the Drazin inverse and its properties. A special case of the Drazin inverse, the group inverse, was introduced and its role in the theory of finite Markov chains examined. An application to linear systems of differential equations was briefly discussed. Finally, three algorithms for its computing have been studied in some detail along with the convergence and some examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:574920
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-07-09 10:08:40