Pseudospectra

Eigenvalues often provide great insight into the behavior of matrices, precisely explaining, for example, the asymptotic character of functions of matrices like A^k and e^tA . Yet many important applications produce matrices whose behavior cannot be explained by eigenvalues alone. In such circumstances further information can be gleaned from broader sets in the complex plane, such as the numerical range (see Chapter 18), the polynomial numerical hull [Nev93], [Gre02], and the subject of this section, pseudospectra.