Applications of Linear Algebra in Information Retrieval

This paper thoroughly analyzes the mathematical principles related to matrices and cosine similarity in the field of information retrieval and their applications in practical scenarios. The article successively introduces the simple matching retrieval method and the relative frequency retrieval method, and focuses on elaborating the cosine similarity retrieval method in detail. By comparing the advantages and disadvantages of the three retrieval methods, the superiority of cosine similarity in semantic understanding and quantitative evaluation is highlighted, while the challenges it faces in high-dimensional data processing are also discussed. With the help of specific cases, this paper vividly demonstrates the practical application of linear algebra in information retrieval. It aims to help readers deeply understand the theoretical value and practical significance of information retrieval and provide valuable references for research and teaching in the field of information retrieval.