Linear Algebra

This course introduces students to fundamental concepts and techniques in linear algebra, a branch of mathematics that deals with vectors, matrices, and linear transformations. It emphasizes understanding vector representations and operations, matrix arithmetic, and methods for solving linear equations. Students learn how to apply matrix operations to perform geometric transformations and explore concepts such as orthogonality, projection, and least squares in vector spaces. The course also covers eigenvalues, eigenvectors, and matrix diagonalization, highlighting their importance in analyzing and simplifying complex systems. Practical applications in fields like computer science, including singular value decomposition and image processing, are integrated to demonstrate the relevance of linear algebra in real-world problems.