The Role of Linear Algebra in Machine Learning Algorithms: A Review

Abstract

Linear algebra forms the mathematical backbone of modern machine learning (ML). Concepts such as matrices, eigenvalues, eigenvectors, and vector spaces are essential for representing data, optimizing models, and enabling efficient computation. This review paper analyzes the role of linear algebraic structures in the design and functioning of ML algorithms. A systematic review methodology is adopted to examine their applications in data representation, dimensionality reduction, optimization, and neural networks. The study highlights that linear algebra not only improves computational efficiency but also enhances model interpretability and scalability.