| Abstract: | In the recent book of R.S. Varga, 3], one of two main recurring themes is that a nonsingular theorem for matrices gives rise to an equivalent eigenvalue inclusion set in the complex plane, and conversely. If such nonsingularity result can be extended via irreducibility, usually this can be used for obtaining more information about the boundary of the corresponding eigenvalue inclusion set. Here we will start with one of Geršgorin‐type theorem for eigenvalue inclusion, given in 1], (for which exists corresponding equivalent statement about nonsingularity of a particular class of matrices) and use it for proving necessary conditions for an eigenvalue to lie on the boundary of localization area. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
