Linear Algebra: Foundations and Modern Applications

Linear algebra is the mathematical engine driving modern technology, from search engine algorithms to the latest developments in artificial intelligence. Understanding these structures is essential for anyone looking to excel in technical fields like data science, physics, or software engineering. This course provides a comprehensive path from basic vector operations to advanced matrix decompositions, ensuring you gain both the theoretical knowledge and the practical intuition required to solve complex problems. You will learn how to: - Understand the core concepts of vectors, matrices, and linear transformations through written theory. - Solve systems of linear equations using Gaussian elimination and matrix inverses. - Explore the properties of vector spaces, including basis, dimension, and orthogonality. - Calculate eigenvalues and eigenvectors to analyze system stability and change. - Apply matrix factorization techniques like Singular Value Decomposition (SVD) for data compression. - Practice interpreting linear algebra within the context of modern machine learning and dimensionality reduction. The course begins with essential terminology and geometric definitions before moving into the mechanics of matrix algebra and abstract spaces. It is designed for beginners who want a clear, step-by-step introduction to the subject with no advanced prerequisites required. Start building your mathematical foundation through structured written explanations and exercises.