This textbook is a comprehensive, practical guide to understanding linear algebra, from fundamental principles to advanced machine learning applications. Designed for students, researchers, and professionals in artificial intelligence, data science, and engineering, it combines mathematical rigor with practical application, using Python and popular libraries such as NumPy, SciPy, Matplotlib, and scikit-learn.
Starting with vectors and matrices, the text moves on to systems of linear equations, transformations, factorizations, eigenvalues, and vector spaces, then expands into orthogonality, matrix factorizations (e.g., SVD, QR, LU), tensors, and optimization. Each concept is presented with clear geometric intuition, detailed examples, and step-by-step Python code. The chapters include visualizations, code outputs, and exercises that strengthen both theoretical understanding and computational skills. Real-world examples show how foundational concepts underpin algorithms in regression, PCA, image compression, neural networks, and more.
This book is suitable both for beginners seeking to understand core ML concepts and for advanced learners exploring spectral methods and tensor decompositions, serving as a versatile, mathematically grounded, code-supported resource.
