Matrix factorization is an important mathematical technique used in data science to represent large and complex datasets in a lower-dimensional form. The fundamental idea is to decompose a matrix into two or more matrices whose product approximates or reconstructs the original data matrix. Techniques such as Singular Value Decomposition (SVD), Non-Negative Matrix Factorization (NMF), and QR factorization have applications in dimensionality reduction, recommendation systems, image processing, text mining, and machine learning. This paper presents the mathematical foundations of matrix factorization, discusses major factorization techniques, and examines their applications in data science. The advantages, limitations, and practical significance of these methods are also discussed. The study demonstrates that matrix factorization provides an effective framework for extracting hidden patterns and reducing computational complexity in high-dimensional datasets.

Keywords: Matrix Factorization, Data Science, Singular Value Decomposition, Non-Negative Matrix Factorization, Dimensionality Reduction, Recommendation Systems, Machine Learning