Linear Algebra

Catalog description

In this course, students examine the fundamental principles of linear algebra in depth. They learn multiple methods for solving systems of linear equations, including Gaussian and Gauss-Jordan elimination, matrix inverses, and LU-factorization. Students perform matrix operations, evaluate determinants and their properties, and construct matrix factorizations. They explore the structure of vector spaces and subspaces, determining bases, dimensions, and ranks. Students also analyze linear transformations by finding their kernels, ranges, and matrix representations. They study eigenvalues, eigenvectors, diagonalization, and orthogonality to deepen their understanding of linear systems and transformations. Finally, students investigate inner product spaces, learning to create orthonormal bases and apply inner product properties to solve least squares problems.