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Linear algebra is a branch of mathematics dealing with vector spaces and linear mappings between such spaces. It forms the theoretical foundation for many applications in computer science, physics, engineering, and other fields. In the context of physical science, linear algebra can be used to model and analyze systems involving vectors and matrices, such as those encountered in quantum mechanics, electromagnetism, and continuum mechanics. In computer science, it finds application in areas like machine learning, computer graphics, and data compression. The subject encompasses various topics including systems of linear equations, vector spaces, determinants, eigenvalues and eigenvectors, orthogonality, and matrix decompositions, among others. These concepts provide a powerful mathematical framework for understanding and solving complex problems in the sciences and engineering.