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undergraduate thesis
Nejednakosti za svojstvene vrijednosti
2020. urn:nbn:hr:126:843811
Đuzel, Monika
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

Cite this document

Đuzel, M. (2020). Nejednakosti za svojstvene vrijednosti (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:843811

Đuzel, Monika. "Nejednakosti za svojstvene vrijednosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:843811

Đuzel, Monika. "Nejednakosti za svojstvene vrijednosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:843811

Đuzel, M. (2020). 'Nejednakosti za svojstvene vrijednosti', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:843811

Đuzel M. Nejednakosti za svojstvene vrijednosti [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 April 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:843811

M. Đuzel, "Nejednakosti za svojstvene vrijednosti", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:843811

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Metadata
TitleNejednakosti za svojstvene vrijednosti
Title (english)Inequalities for Eigenvalues
AuthorMonika Đuzel
MentorDarija Marković (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Tema ovog rada su nejednakosti za svojstvene vrijednosti. Najprije ćemo navesti pojmove koji će nam biti potrebni u kasnijim računima i dokazima. Govorit ćemo o svojstvenim i singularnim vrijednostima te dokazati teorem koji ih povezuje nejednakostima. Nakon toga dokazat ćemo teorem o monotonosti za singularne i svojstvene vrijednosti. Dotaknut ćemo se i teme teorema o ispreplitanju za singularne i svojstvene vrijednosti. Također, dokazat ćemo i Courant-Fischerov teorem za svojstvene i singularne vrijednosti. Iskazat ćemo Poincareov teorem, Hornov teorem i Von Neumannov teorem. Dokazat ćemo da je tr (AX) = 0 za sve hermitske matrice X ako i samo ako je A = 0 te da je tr (AX) realna za sve hermitske matrice X ako i samo ako je A hermitska.
Abstract (english)
The subject of this paper are inequalities for eigenvalues. First of all, we will define terms that will be used in this paper. We are going to discuss eigenvalues, singular values and prove a theorem that relates specified values to inequalities. Afterwards, monotonicity theorems for singular and eigenvalues will be proven. We will also refer to a subject of interlace theorems for singular and eigenvalues. Furthermore, the Courant-Fischer theorem for eigenvalues and singular values will be proven. We will state Poincare’s theorems, Horn’s and Von Neumann’s theorem. It will be shown that tr (AX) = 0 for all Hermitian matrices if and only if A = 0 and also that tr (AX) = 0 for all Hermitian matrices X if and only if A is Hermitian.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:843811
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 on2020-10-30 07:39:48