Linear Algebra and Applications

This program is primarily for graduate students of IMA Participating Institutions. The NSF may provide support for a limited number of students at other US universities. In order to participate, students need to fill out the application form and provide a letter of nomination.

From Monday, June 30 through Friday, July 25, 2008, Iowa State University will be the host of the Institute for Mathematics and its Applications (IMA) Summer Graduate Program in Mathematics. The course will concentrate on Linear Algebra and Applications.

Program Description:

Linear algebra is a subject of central importance in both mathematics and a variety of other disciplines. Research in linear algebra is very active, with a wealth of applications, and linear algebra is also a powerful tool for research in other areas. The program will run for four weeks and cover linear algebra, numerical linear algebra, and applications. Four topics will be covered, one per week. Each of the speakers will present open research questions toward the end of the week, and it is our goal to have each student involved in at least one research problem during the course of the workshop.

• Week 1: Linear algebra and applications to combinatorics, taught by Bryan Shader. Combinatorial matrix theory, encompassing connections between linear algebra, graph theory, and combinatorics, has emerged as a vital area of research over the last few decades, having applications to fields as diverse as biology, chemistry, economics, and computer engineering. ..more »


• Week 2: Numerical linear algebra, taught by David S. Watkins. The ability to carry out matrix computations numerically, with accuracy and efficiency, is essential for applications. ..more »


• Week 3: Matrix inequalities in science and engineering, taught by Chi-Kwong Li. Matrix inequalities have applications to many branches of pure and applied areas, including quantum computing, mathematical biology, perturbation theory, optimal parameters in iterative methods and optimization problems in distance-squared matrices. ..more »


• Week 4: Applications of linear algebra to dynamical systems, taught by Fritz Colonius. Linear algebra is a key tool in the study of ordinary differential equations, including the explicit form of solutions to linear equations, linearization theory, and results on invariant manifolds and the Grobman-Hartman theorem. ..more »

It is expected that participants will have had standard undergraduate courses in linear algebra, numerical analysis and ordinary differential equations. Some exposure to canonical forms and matrix factorization would be helpful, although these topics will be reviewed as needed, especially in week one.