Nearly defective complex eigenvalues in Bessel matrices Original Research Article

It is known that an n×n Bessel matrix Tn exhibits simple well-separated complex eigenvalues which are getting more and more ill-conditioned for increasing n. The aim of this paper is to study the behavior of such eigenvalues, which are simple in theory, but in practice become defective using finite precision. To this end we provide a sharp estimate of the distance of Tn to the nearest defective matrix, when n increases.