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undergraduate thesis
Generalizirani svojstveni problem i definitni matrični parovi
2017. urn:nbn:hr:126:366332
Pilj, Marinela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Geometry and Mathematics Teaching Mathematics Research Group

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Pilj, M. (2017). Generalizirani svojstveni problem i definitni matrični parovi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:366332

Pilj, Marinela. "Generalizirani svojstveni problem i definitni matrični parovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:366332

Pilj, Marinela. "Generalizirani svojstveni problem i definitni matrični parovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:366332

Pilj, M. (2017). 'Generalizirani svojstveni problem i definitni matrični parovi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:366332

Pilj M. Generalizirani svojstveni problem i definitni matrični parovi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 April 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:366332

M. Pilj, "Generalizirani svojstveni problem i definitni matrični parovi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:366332

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Metadata
TitleGeneralizirani svojstveni problem i definitni matrični parovi
Title (english)Generalised Eigenvalue Problem and Definite Matrix Pairs
AuthorMarinela Pilj
MentorIvana Kuzmanović (mentor)
MentorMarija Miloloža Pandur (komentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Geometry and Mathematics Teaching Mathematics Research Group)
Osijek
Defense date and country2017-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovome radu ponovit ćemo kako definiramo osnovni svojstveni problem za matricu, pojmove svojstvenih vrijednosti, svojstvenih vektora i karakterističnog polinoma matrice. U usporedbi s time, uvest ćemo pojam generaliziranog svojstvenog problema za matrični par te također definirati svojstvene vrijednosti, svojstvene vektore i karakteristični polinom matričnog para. Pokazat ćemo koji se sve problemi mogu pojaviti kod generaliziranog svojstvenog problema, a kojih nema u svojstvenom problemu za matricu. Definirat ćemo regularan i singularan matrični par, ekvivalentne i kongruentne matrične parove te pokazat što ti pojmovi znače za generalizirani svojstveni problem. U drugome dijelu bavit ćemo se generaliziranim svojstvenim problemom matričnog para za koji postoji realna linearna kombinacija danih matrica koja je pozitivno definitna, tzv. definitnog para. Za kraj ćemo dati važne teoreme o istovremenoj dijagonalizaciji definitnih matričnih parova.
Abstract (english)
In this paper we will restate how ordinary eigenvalue problem for a given matrix is defined, as well as the terms of eigenvalues, eigenvectors and characteristic polynomial of matrix. Compared to that, we will introduce the term of generalized eigenvalue problem for matrix pair, and also define eigenvalues, eigenvectors and characteristic polynomial of matrix pair. We will show all problems that can appear in the generalized eigenvalue problem, but which do not exist in eigenvalue problem for matrix. We will define regular and singular matrix pair, equivalent and congruent matrix pairs and show what this concepts mean for generalized eigenvalue problem. In second part, we will deal with generalized eigenvalue problem for matrix pair for which exists real linear combination of given matrices which is positive definite, so called, definite pair. At the end of the paper, we will give important theorems about simultaneous diagonalization of definite matrix pairs.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:366332
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-06 07:00:51