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undergraduate thesis
SVD dekompozicija i primjene
2018. urn:nbn:hr:126:714160
Hrnjkaš, Mihaela
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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Hrnjkaš, M. (2018). SVD dekompozicija i primjene (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, Mihaela. "SVD dekompozicija i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, Mihaela. "SVD dekompozicija i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš, M. (2018). 'SVD dekompozicija i primjene', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 12 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:714160

Hrnjkaš M. SVD dekompozicija i primjene [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2025 January 12] Available at: https://urn.nsk.hr/urn:nbn:hr:126:714160

M. Hrnjkaš, "SVD dekompozicija i primjene", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:714160

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Metadata
TitleSVD dekompozicija i primjene
Title (english)SVD Decomposition and Applications
AuthorMihaela Hrnjkaš
MentorZoran Tomljanović (mentor)
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 country2018-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U prvome dijelu ovoga rada definirat ćemo pojam dekompozicije na singularne vrijednosti te iskazati i dokazati teorem koji govori o egzistenciji ove dekompozicije. Spomenut ćemo neka od najvažnijih svojstava te uočiti poveznicu između singularnih i svojstvenih vrijednosti. U drugome dijelu rada dotaknut ćemo se primjena dekompozicije na singularne vrijednosti. Ukratko ćemo se upoznati s linearnim problemom najmanjih kvadrata te opisati primjenu SVD dekompozicije. Spomenut ćemo kompresiju slike te na primjeru ilustrirati primjenu dekompozicije na singularne vrijednosti u kompresiji koristeći se svojstvom aproksimacije matricom nižeg ranga.
Abstract (english)
In the first part of this paper, we will define the concept of singular value decomposition and prove the theorem that states the existence of singular value decomposition. Some of the most important properties will also be mentioned and connection between eigenvalues and singular values will be noticed. In the second part of the paper, attention will be given to applications of singular value decomposition. A brief introduction to linear least square problem will be followed by application of singular value decomposition to this problem. Also, we will touch upon an image compression and illustrate the usage of SVD decomposition in compression using the property of a low-rank matrix approximation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:714160
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 on2018-10-18 06:11:02