This textbook is a comprehensive, application-driven guide to mastering linear algebra from foundational principles to advanced machine learning applications. Designed for students, researchers, and professionals in AI, data science, and engineering, the book blends mathematical rigor with practical implementation using Python and popular libraries such as NumPy, SciPy, Matplotlib, and scikit-learn. Starting with vectors and matrices, the text builds toward systems of linear equations, transformations, determinants, eigenvalues, and vector spaces—then extends to orthogonality, matrix factorizations (e.g., SVD, QR, LU), tensors, and optimization. Each concept is introduced with clear geometric intuition, detailed examples, and step-by-step Python code. Chapters include visual illustrations, code outputs, and exercises that reinforce both theoretical understanding and computational skills. Real-world examples show how core concepts underpin algorithms in regression, PCA, image compression, neural networks, and more. This book is suitable for either beginner aiming to grasp key ML concepts or an advanced learner exploring spectral methods and tensor decompositions, this book serves as a flexible resource, grounded in mathematics, empowered by code.