20.500.12556/RUL-120459 Popolnoma pozitiven rang simetričnih matrik delo diplomskega seminarja The completely positive rank of symmetric matrices V delu diplomskega seminarja bomo obravnavali popolnoma pozitivne matrike in njihov popolnoma pozitiven rang. Dva s tem povezana problema o določanju popolne pozitivnosti matrike in izračunljivosti njenega popolnoma pozitivnega ranga sta še vedno odprta, zato bomo sprva predstavili glavne definicije in rezultate na temo popolnoma pozitivnih matrik. Ogledali si bomo povezavo med popolnoma pozitivnimi matrikami, M-matrikami in diagonalno dominantnimi matrikami ter geometrijski pogled na popolnoma pozitiven rang. Nato si bomo pogledali alternativen postopek iskanja omejitev popolnoma pozitivnega ranga matrik s pomočjo teorije grafov. Natančneje, podali bomo lastnosti pripadajočih grafov, ki omejijo popolnoma pozitiven rang matrik pripadajočih vzorcev. In this thesis, we will investigate the completely positive matrices and their completely positive rank. The problems of determining whether a matrix is completely positive and computing its completely positive rank are still open. We will first present the main definitions and known results of this topic. We will also present M-matrices, diagonally dominant matrices, and discuss the geometric approach to complete positivity. Furthermore, we will take a look at the alternative procedure of finding constraints of the completely positive rank of matrices using graph theory. In particular, we will define the characteristics of the corresponding graphs which bound the completely positive rank of the matrix. popolnoma pozitivne matrike popolnoma pozitiven rang pozitivno semidefinitne matrike M-matrike konveksni stožci pokritje grafa s klikami completely positive matrices completely positive rank positive semidefinite matrices M-matrices convex cones clique covering number true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-20 08:15:15 2020-09-20 08:15:19 2024-05-29 14:33:08 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 110968 58094851 1452.pdf 1452.pdf 1 2A21C07C74400A64A1701CAD372B82AE 9ebfe060d81acfb634a7781c08631e0f3316ceb86f7acc887b2ad99fbd4e798c 17dc9ce7-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=135254 Fakulteta za matematiko in fiziko 0 0 0