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undergraduate thesis
Spektar i pseudospektar matrice
2021. urn:nbn:hr:126:874223
Majdenić, Dunja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Majdenić, D. (2021). Spektar i pseudospektar matrice (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:874223

Majdenić, Dunja. "Spektar i pseudospektar matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:874223

Majdenić, Dunja. "Spektar i pseudospektar matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:874223

Majdenić, D. (2021). 'Spektar i pseudospektar matrice', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:874223

Majdenić D. Spektar i pseudospektar matrice [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:126:874223

D. Majdenić, "Spektar i pseudospektar matrice", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:874223

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Metadata
TitleSpektar i pseudospektar matrice
Title (english)Spectrum and Pseudospectrum of a Matrix
AuthorDunja Majdenić
MentorIvana Kuzmanović Ivičić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U završnom radu definirat ćemo pojam svojstvenih vrijednosti matrice, svojstvene vektore, spektar matrice te svojstveni polinom. Također ćemo definirati algebarsku i geometrijsku kratnost svojstvenih vrijednosti te pokazati njihovu ulogu u utvrđivanju dijagonalizabilnosti matrice. Opisat ćemo spektar posebnih tipova matrica štoćemo potkrijepiti i primjerima. Definirat ćemo Jordanovu formu matrice i slijedom primjera prikazati njeno određivanje. Uvodimo pojam pseudospektra koje je zapravo poopćenje pojma spektra matrice. Ustanovitćemo da pseudospektar ovisi o normi i da je presjek svih pseudospektara matrice upravo spektar matrice. Prikazatćemo svojstva pseudospektra.
Abstract (english)
In this nal paper we will dene the concept of eigenvalues and eigenvectors of the matrix, the spectrum of the matrix and characteristic polynomial of the matrix. We will also dene the algebraic and geometric multiplicity of eigenvalues and show their role in determining the diagonalizable of a matrix. We will describe a spectrum of special types of matrices what we will substantiate with examples. We will dene Jordan form of the matrix and show its computation by example. We introduce the concept of a pseudospectrum which is actually generalization of the concept of a matrix spectrum. The pseudospectrum depends on the norm and the intersection of all pseudospectra of the matrix is the spectrum of the matrix. The properties of the pseudospectrum are given.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:874223
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 on2021-10-25 07:44:28