On some properties of the pseudospectral radius
G. Kumar, S. Lui · Electronic Journal of Linear Algebra · 2014
Pseudospectra provide an analytical and graphical alternative for investigating non- normal matrices and operators, give a quantitative estimate of departure from non-normality and give information about stability. In this paper, we prove that pseudospectral radius is sub-additive and sub-multiplicative for a commuting pair of matrices over the complex field, extending the same result for spectral radius. We discuss the same result for a non-commutative pair of matrices. We also give an analogue of the spectral radius formula for pseudospectrum.