Norm behavior of Jordan and bidiagonal matrices

Determining the norm behavior of non-normal matrices from the sets related to the spectrum is one of the fundamental problems of matrix theory. This article proves that the pseudospectra and condition spectra determine the norm behavior of Jordan matrices for any matrix p-norm. Further, sufficient conditions for determining the 1-norm and infinity norm behavior of bidiagonal matrices from the pseudospectra and condition spectra are also provided.