Course Description: Linear Algebra is a foundational branch of mathematics that deals with vector spaces, linear transformations, and systems of linear equations. It serves as a powerful tool in numerous fields, including computer science, economics, engineering, data science, and natural sciences. This course focuses on the fundamental concepts and computational techniques necessary for solving linear equations and understanding vector spaces and matrix operations.

Throughout the course, students will develop proficiency in working with matrices, determinants, vector spaces, eigenvalues, and eigenvectors. They will learn to apply these concepts to real-world problems, such as network analysis, optimization, and computer graphics. They will explore various theoretical applications to deepen their understanding of the subject.

By the end of the course, students will have mastered key topics in Linear Algebra, including systems of linear equations, matrix algebra, vector spaces, inner product spaces, linear transformations, and diagonalization. They will also gain insight into advanced applications, such as singular value decomposition (SVD) and the spectral theorem, which are crucial for machine learning and data analysis.