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master's thesis
Normalne matrice
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:325049
Šimić, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šimić, A. (2017). Normalne matrice (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:325049

Šimić, Ana. "Normalne matrice." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:325049

Šimić, Ana. "Normalne matrice." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:325049

Šimić, A. (2017). 'Normalne matrice', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:325049

Šimić A. Normalne matrice [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:325049

A. Šimić, "Normalne matrice", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:325049

Metadata
TitleNormalne matrice
AuthorAna Šimić
MentorRajna Rajić (mentor)
Committee memberRajna Rajić (predsjednik povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberVjeran Hari (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog rada su normalne matrice. U prvom poglavlju rada prikazujemo osnovne rezultate o normalnim matricama. Dajemo neke karakterizacije normalnih matrica. Razmatramo (0,1)-matrice te dajemo dovoljan uvjet za njihovu normalnost. Također razmatramo nejednakosti koje uključuju elemente matrica te svojstvene i singularne vrijednosti matrica. Slučajevi jednakosti u tim nejednakostima rezultiraju normalnošću matrica. Neki rezultati o normalnim matričnim pertubacijama su također prikazani. Drugo poglavlje usmjereno je na podklasu normalnih matrica, unitarne matrice. Prikazujemo osnovna svojstva unitarnih matrica, raspravljamo o strukturi realnih ortogonalnih matrica s obzirom na transformacije sličnosti, povezujemo kontrakcije s unitarnim matricama, te prezentiramo nejednakost koja povezuje prosječne svojstvene vrijednosti svake od dviju unitarnih matrica s prosječnom svojstvenom vrijednosti njihovog umnoška.
Abstract (english)
The subject of this work is normal matrices. In the first chapter of this work we present basic results on normal matrices. We give some characterizations of a normal matrix. We consider (0; 1)-matrices, and give a sufficient condition on their normality. We also consider the inequalities involving entries, eigenvalues and singular values of matrices. The equality cases of these inequalities result in the normality of the matrices. Some results on normal matrix pertubations are presented as well. The second chapter focuses on a subclass of normal matrices, unitary matrices. We present basic properties of unitary matrices, discuss the structure of real orthogonal matrices under similarity, deal with the connections of contractions with unitary matrices, and present an inequality relating the average of the eigenvalues of each of two unitary matrices to that of their product.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:325049
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-03-22 09:47:22