霍奇排名是在近幾年才運用在排名的一種方法。在大多數現在的資料庫 中,資料庫很龐大,有些甚至會需要網路連結,而且很多會有資料不完整或 是資料不平衡的狀況。我們選擇用霍奇排名這種排名方法來處理可能會遇到 的這些困擾。 這篇論文主要目的是想用運用基本的線性代數來研究霍奇排名和推導組合霍奇理論。 / HodgeRank is a method of ranking that is new in recent years. In most of modern datasets, the amount of data is very large, some also need the internet connection, and plenty of them have the feature that incomplete or imbalanced. We use the method of HodgeRank to deal with these difficulties. This thesis is primary using elementary linear algebra to survey HodgeRank and deduce the combinatorial Hodge Theorem.