Introduction to Linear Algebra for ML

Mathematics is the universal language of science and technology, providing tools to model natural phenomena, design algorithms, and extract insights from data. Among its branches, linear algebra stands out as a cornerstone for ML, enabling the representation, manipulation, and analysis of high-dimensional data. The term “linear” derives from the Latin linearis, meaning “pertaining to lines,” and refers to relationships that preserve proportionality, such as straight lines in geometry or linear transformations in algebra. The term “algebra,” from the Arabic al-jabr (“reunion of broken parts”), denotes the manipulation of symbols and equations to solve problems systematically. This chapter introduces linear algebra’s role in ML, offering a high-level overview of key concepts and Python tools, along with guidance on using this book. Designed for undergraduate and early graduate students, this book sets the foundation for subsequent chapters that explore vectors, matrices, linear systems, linear transformations, determinants, eigenvalues, eigenvectors, vector spaces, orthogonality, matrix factorization, optimization, and advanced applications in detail.