This accessible yet rigorous textbook introduces the fundamentals of linear algebra in the context of real-world data science applications. Including the latest developments in the field, clear and detailed mathematical explanations. and extensive examples, it offers a comprehensive and approachable introduction to the subject, focusing on the foundations of the singular value decomposition and its many uses. Key topics include matrix subspaces, reduced-rank matrix approximation, angles between subspaces, averaging subspaces, spectral embedding algorithms including Laplacian eigenmaps and multidimensional scaling, the K-SVD dictionary learning algorithm, and the generalized singular value decomposition. The text takes a practical approach, featuring real-world application examples and more than 600 end-of-chapter exercises. Accompanying online resources include a solutions manual for instructors, data sets, and MATLAB and Python code for implementing algorithms in the text.