Linear Algebra for Data Science and AI Book 3. Spectral Methods and Matrix Decompositions

Linear Algebra for Data Science and AI: Book 3. Spectral Methods and Matrix Decompositions (Linear Algebra for Data Science & AI)
English | January 14, 2026 | ASIN: B0GGTK8G9H | 285 pages | Epub | 9.82 MB
Linear Algebra for Data Science and AI is a five-book textbook series designed to take readers from a first encounter with linear algebra to a level of conceptual mastery that supports advanced study and research in data science and AI. The series emphasizes clear, intuitive explanation in words-supported by rigorous definitions and carefully chosen formulas-so that readers can understand not only how linear algebra is written, but what it means.This series is theory- and concept-driven. It does not include coding, AI implementation, or drill-style calculation practice. Instead, each topic is motivated by how it appears in machine learning, deep learning, and modern data analytics, helping readers connect abstract ideas to practical meaning while building a durable foundation across the five volumes.Book 3 introduces spectral thinking and the decomposition toolkit that powers modern data science. You will learn eigenvalues and eigenvectors, diagonalization, and the spectral theorem, then move to singular value decomposition (SVD) as a universal tool for dimensionality reduction, low-rank approximation, denoising, and conditioning. The book also covers core factorizations such as QR and Cholesky, and connects decompositions to practical modeling assumptions. The focus remains conceptual and theory-driven, with careful verbal explanation and no coding or drill-style computation.