M 333 Linear Algebra
Prerequisite: M 172
Covers linear systems and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and orthogonality. Exact topics may vary year to year.
Knowledge of the formal development of the theory of abstract vector spaces, their subspaces, and dimension.
Ability to deal with linear transformations on various spaces and their matrix representations in different bases.
Understanding of inner product spaces and normed spaces, including different norms of linear transformations.
Understanding of the theoretical basis for selecte-d applied techniques, as exemplified by the least squares approximation and the singular value decomposition.
Ability to explore and prove simple conjectures and comprehend moderately complex proofs in the above areas.understand the basic concepts in geometry,