Spectra and pseuduospectra of matrices۱

Given A ∈ Mn(C) and ε > ۰ be given. The ε-pseudospectrum of A is defined tobe the set(...)The concept of pseudospectra has its roots in the study of the behavior of non-normalmatrices and their spectra. One of the early works on pseudospectra was done in ۱۹۶۷by Jim Varah in his Stanford PhD thesis. The idea was further developed by otherresearchers, among them Lloyd N. Trefethen and Mark Embree who published a bookin ۲۰۰۵ entitled Spectra and Pseudospectra.In this lecture we review recent results in spectra and ε-pseudospectra of matrices.Also, we study the shapes and behavior of the connected components of ε-pseudospectra for special kinds of matrices. Moreover, growth rate of ε-pseudospectrais considered.