Application of linear algebra in a ranking method on a selected sport

Metoda razvrščanja temelji na linearni algebri. Za uporabo metode na šport, moramo sprva definirati ustrezen matematični model. Vzeti moramo množico tekmovalcev. Znotraj te množice se vsak tekmovalec pomeri z vsakim tekmovalcem, kjer vedno dobimo zmagovalca in poraženca dvoboja. Igralci lahko drug proti drugemu odigrajo tudi več tekem. Zmage in poraze zapišemo s pomočjo incidenčne matrike, kjer enica predstavlja zmago in ničla poraz. Potek igre lahko tudi ponazorimo s pomočjo usmerjenega grafa. Začetek povezave predstavlja zmagovalca dvoboja, konec povezave pa poraženca. Vozlišča so tekmovalci. Rezultat vsakega športnika dobimo kot rešitev ustreznega sistema linearnih enačb. Pri izbiri športa moramo biti pozorni na to, da v igri oziroma dvoboju ni možno dobiti izenačenega izida, sicer ne bi mogli uporabiti metode razvrščanja. Navedenim parametrom in pogojem ustreza šport, na katerem sem uporabila opisano metodo. Izbrani šport je paralelno deskanje na snegu, kjer v drugem delu diplomske naloge opisujem in analiziram dobljene rezultate.The ranking method is based on linear algebra. In order to apply the method to a sport, an adequate mathematical model must be defined. We have to take a set of competitors. Within this set, all competitors must compete against each other therefore, a winner and a loser are obtained in every match. Competitors can also play several matches against each other. Victories and defeats will be marked using the incidence matrix - number one represents a victory and zero represents a defeat. The course of the game can also be illustrated by a directed graph. The beginning of the connection represents the winner of the duel, and the end of the connection represents the loser. The vertices are represented by the players. The result of each athlete is obtained as a solution of the corresponding system of linear equations. When choosing a sport, we must pay attention to the fact that the game does not end in a tie, otherwise the ranking method cannot be applied. The stated parameters and conditions are satisfied by the sport on which I applied the described method. The chosen sport is parallel snowboarding. In the second part of the thesis I describe and analyze the obtained results