DEPARTMENT of MATHEMATICS Structured Inverse Eigenvalue Problems

Structured Inverse Eigenvalue Problems
Dr. Keivan Hassani Monfared
Western Illinois University
Abstract: Dynamical systems are everywhere, so too are the
differential equations describing them. In this talk, rather
than trying to find a solution to a systems of differential
equations, in a combinatorial-matrix-theoretic approach we
study what conditions on the expected behavior of a dynamical system guarantee the existence of a system with that given
behavior. Certain behaviors of dynamical systems can be described by their natural frequencies, i.e. the eigenvalues of
the coefficient matrix in the matrix form of the system of
differential equations, where the coefficient matrix has a specific ’structure’. Such problems are called structured inverse
eigenvalue problems (SIEP). Using the Jacobian method we
show that for any given set L of n distinct real numbers, and
any given graph G, there is a real symmetric matrix of order
n whose graph is G, and its spectrum is L. Moreover, if G
is connected, one can choose this matrix so that none of its
eigenvectors have a zero entry.
October 30, 2014
3:45 p.m.
Morgan Hall 204
will be served at 3:30