Eigenvalues give deep insight into the behavior of linear dynamical systems and many other phenomena. However, for many matrices or operators that are nonsymmetric (or non-self-adjoint), these eigenvalues do not give a complete understanding of dynamics. Moreover, small changes to the matrix or operator can induce large changes in the eigenvalues.
Professor Embree studies problems in numerical linear algebra, spectral theory, and applications that involve the computation and analysis of eigenvalues. Topics range from quasicrystal models in mathematical physics, to convergence theory for eigenvalue computation, to the construction of reduced order models for large-dimensional dynamical systems. Recent themes include differential algebraic equations, nonlinear eigenvalue problems, and low-rank approximation of large data sets.
Professor Embree also leads Virginia Tech's program in Computational Modeling and Data Analytics (CMDA).