Linear Algebra

This module presents the mathematical foundations of linear algebra, including a review of basic matrix algebra and linear systems of equations as well as basics of linear transformations in Euclidean spaces, determinants, and the Gauss-Jordan Algorithm. The more substantial part of the module begins with abstract vector spaces and the study of linear independence and bases. Further topics may include orthogonality, change of basis, general theory of linear transformations, eigenvalues, eigenvectors, as well as applications to least-squares approximations and Fourier transforms, differential equations, and computer graphics.