In this paper we will first introduce the singular value decomposition (SVD) of a matrix and basic theory behind it. We will then go over the general algorithm, along with implementations in SAGE and computational efficiency comparisons with built in libraries. At the end we will discuss principal component analysis and its relation with the SVD as one of many applications.

Adopting a corpus-based approach, this paper aims to explore the different meaning and usages between the two Chinese near-synonymous verbs of running: Ben and Pao following the model: Module-Attribute Representation of Verbal Semantics (MARVS) proposed by Huang at all in 2000. This study proposes that Pao has the event focus of the endpoint of the event, but Ben does not. Besides, Ben always e...