prikaz prve stranice dokumenta Tenzorske algebre i primjene
  Download
PDF 309.2 KB
master's thesis
Tenzorske algebre i primjene
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:743508
Brozović, Bruna
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Brozović, B. (2024). Tenzorske algebre i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:743508

Brozović, Bruna. "Tenzorske algebre i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:743508

Brozović, Bruna. "Tenzorske algebre i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:743508

Brozović, B. (2024). 'Tenzorske algebre i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 09 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:743508

Brozović B. Tenzorske algebre i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2025 January 09] Available at: https://urn.nsk.hr/urn:nbn:hr:217:743508

B. Brozović, "Tenzorske algebre i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:743508

Metadata
TitleTenzorske algebre i primjene
AuthorBruna Brozović
MentorDražen Adamović (mentor)
Committee memberDražen Adamović (predsjednik povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-11-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavni cilj ovog rada bio je prikazati osnovnu teorijsku pozadinu tenzorske algebe. Uz opisan tenzorski produkt i osnovne objekte algebre, konstruirana je tenzorska algebra \(T(E)=\bigoplus\limits_{r=0}^{\infty}T^r(E)\) i dokazano je njeno univerzalno svojstvo, točnije da dijagram komutira. Konstruirana je i kvocijentna algebra \(S(E)=T(E)/M(E)\), poznata kao i simetrična algebra. Za kraj je dan kratak pregled primjene tenzora u ekonomiji kroz Bayesov autoregresivni tenzorski model.
Abstract (english)
The main goal of this thesis was to present the fundamental theoretical background of tensor algebra. Alongside a description of the tensor product and basic algebraic objects, the tensor algebra \(T(E)=\bigoplus\limits_{r=0}^{\infty}T^r(E)\) is constructed, and its universal property is proven, specifically that the diagram commutes. Additionally, the quotient algebra \(S(E)=T(E)/M(E)\), also known as the symmetric algebra, is constructed. Finally, a short overview of tensor applications in economy is provided, with a focus on the Bayesian autoregressive tensor model.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:743508
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) icon
Created on2024-11-12 12:41:27