MATH 390

Advanced Linear Algebra

This course begins as a review and continuation of MATH 290: Linear Algebra. Topics covered include invariant subspaces, Jordan canonical form, and rational canonical forms of linear transformations. The remainder of the course is split between advanced topics and applications. Advanced topics include decompositions (such as the LU decomposition), principal axis theorem, alternate definitions of the determinant, singular values, and quadratic forms. Applications include topics such as least-squares fit, error-correcting codes, linear programming, physical problems employing eigenvalues, Markov chains, and secret sharing.

Prerequisites: MATH 290 with grade of C- or higher