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undergraduate thesis
Nenegativne i M - matrice
2019. urn:nbn:hr:126:698540
Crnobrnja, Tea
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

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Crnobrnja, T. (2019). Nenegativne i M - matrice (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:698540

Crnobrnja, Tea. "Nenegativne i M - matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:698540

Crnobrnja, Tea. "Nenegativne i M - matrice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:698540

Crnobrnja, T. (2019). 'Nenegativne i M - matrice', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 02 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:698540

Crnobrnja T. Nenegativne i M - matrice [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2025 February 02] Available at: https://urn.nsk.hr/urn:nbn:hr:126:698540

T. Crnobrnja, "Nenegativne i M - matrice", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:698540

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Metadata
TitleNenegativne i M - matrice
Title (english)Nonnegative and M- Matrices
AuthorTea Crnobrnja
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 country2019-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovome radu proučavat čemo posebnu kategoriju matrica. Definirat ćemo nenegativne matrice te uvesti pojam M–matrice. Navest ćemo primjere te karakterizaciju navedenih matrica. Promotrit ćemo nenegativne matrice čiji inverzi su M–matrice. Ako je A nenegativna matrica reda n i \(A^{-1}\) je M–matrica, onda su gotovo glavni minori od A svakog reda nenegativni. Pokazat ćemo da je nesingularna matrica A reda p inverzna M–matrica ako i samo ako je \(Q^{T}AQ + D\) inverzna matrica reda n, pri čemu je Q nenegativna matrica dimenzija p × n, s točno jednim pozitivnim elementom u svakom stupcu i D je pozitivna dijagonalna matrica. Ovo obuhvaća nekoliko činjenica o inverzima M–matrica kao posebnim slučajevima.
Abstract (english)
This paper studies special matrix categories. We will define nonegative and introduce the term M–matrices. A characterization of a class of totally nonnegative matrices whose inverses are M–matrices is given. It is then shown that if A is nonnegative of order n and \(A^{-1}\) is an M–matrix, then the almost principal minors of A of all orders are nonnegative. We show that a nonsingular p-by-p matrix A is an inverse M–matrix if and only if \(Q^{T}AQ + D\) is an n-by-n inverse M–matrix whenever Q is a p-by-n nonnegative matrix with exactly one positive entry in each column and D is a positive diagonal matrix. This includes few facts about inverse M–matrices as special cases.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:698540
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
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Created on2019-10-21 06:08:15