Ranking is a ubiquitous problem appearing in many real-world applications. The superior players or objects are oftentimes determined by a matchup or pairwise comparison. Various models have been developed to integrate the matchup results into a single ranking list of players and to further predict the results of future matchups. Amongst them, the Bradley-Terry model is a mainstream model that achieves the goals by constructing explicit probabilistic interpretation. However, the model suffers from its strong assumption of transitive relationships and becomes vulnerable in practices where intransitive relationships exist. Blade-Chest model is an alternative solution to this intransitivity challenge by allowing the multi-dimensional representation of players. In this paper, we propose a low-rank matrix approach to characterize all players and generalize the related works by introducing a unified framework. Our experimental results on synthetic datasets and real-world datasets show that the proposed model is stably competitive with the standard models in terms of the consistency of probabilistic model interpretation and the predictive performance in out-of-sample tests.