#### Abstract Title

#### Institution

Young Harris College

#### Abstract

In this talk, we discuss an isospectral flow in the space of matrices, which deforms any given real banded matrix with a simple real spectrum to a symmetric matrix. We prove that if the initial condition A0 is banded matrix with lower bandwidth p = 2 and upper bandwidth q = 0 with simple real spectrum and second subdiagonal elements different from zero, then its omega-limit set is a pentadiagonal symmetric matrix isospectral to A0 and it has the same sign pattern in the second subdiagonal elements as the initial condition A0. We provide some simulation results to highlight some aspects of this nonlinear system. As an application, we prove that this flow provides the solution of an infinite-time horizon optimal control problem.

An Isospectral Flow on Banded Matrices and Its Optimality

In this talk, we discuss an isospectral flow in the space of matrices, which deforms any given real banded matrix with a simple real spectrum to a symmetric matrix. We prove that if the initial condition A0 is banded matrix with lower bandwidth p = 2 and upper bandwidth q = 0 with simple real spectrum and second subdiagonal elements different from zero, then its omega-limit set is a pentadiagonal symmetric matrix isospectral to A0 and it has the same sign pattern in the second subdiagonal elements as the initial condition A0. We provide some simulation results to highlight some aspects of this nonlinear system. As an application, we prove that this flow provides the solution of an infinite-time horizon optimal control problem.