Some remarks on a theorem of Gudkov Original Research Article

We survey a nonsingularity criterion due to Gudkov. Firstly, adopting Beauwensʹs concept of semistrict diagonal dominance, we modify the criterion in order to cover a class of matrices larger than the class covered originally. Secondly, we exploit Gudkovʹs theorem for bounding an isolated eigenvalue and investigating the structure of the corresponding eigenvector.