About This Course

 Computational Linear Algebra is a foundational course designed to bridge the gap between classical linear algebra theory and modern computational practice. As data-driven technologies continue to reshape engineering, science, and industry, the ability to translate mathematical concepts into efficient algorithms has become an essential skill. This course equips students with both the conceptual understanding and hands-on experience needed to analyze, model, and solve real-world problems using matrices, vectors, and numerical methods. Students will learn how linear algebra powers applications such as data analysis, machine learning, scientific computing, and image processing. The course emphasizes not only how to perform matrix computations, but also how to evaluate their numerical accuracy, stability, and efficiency.

 Throughout the course, students gain practical experience implementing algorithms in MATLAB. Each module blends mathematical principles with computational techniques—starting from matrix operations and Gaussian elimination, progressing through vector spaces and orthogonality, and moving into eigenvalues, eigenvectors, and singular value decomposition (SVD). Real applications, such as principal component analysis (PCA), least-squares regression, and image compression, help students understand how matrix decompositions drive modern data science workflows. By working through labs and numerical experiments, students develop intuition about how algorithms behave on real data and how computational errors can influence results.

 By the end of the course, students will be able to analyze linear systems, apply orthogonalization methods, implement decomposition techniques, and use matrix factorization to extract insights from data. They will also learn how to evaluate the conditioning of problems, choose appropriate numerical methods, and write efficient computational solutions. The course prepares students for advanced study in machine learning, optimization, scientific computing, and artificial intelligence, and provides essential skills for careers in data science, analytics, and engineering.