Linear Algebra is an essential foundational course whose core objective is to help students master the fundamental concepts and methods of vector spaces and matrix computations, and to apply them proficiently to solve real-world problems. The course will guide students through methods for solving linear systems, such as Gaussian elimination and matrix factorization, and help them become familiar with matrix operations, determinant calculations, and their geometric meanings. In addition, students will learn the concept of linear transformations and express them in matrix form, gaining a deeper understanding of key ideas such as eigenvalues and eigenvectors and their applications. The course emphasizes connecting theory with practice, illustrating the wide-ranging applications of linear algebra in engineering, science, and economics through real examples. Topics include practical cases in data analysis, machine learning, image processing, and physical simulation, helping students build strong links between mathematical concepts and real-world problems.

Ron Larson, Elementary Linear Algebra (Metric Version), 8/e, Cengage Learning, 2024.