Geodesic
Partition of the spectrum by Hermite forms and one-dimensional spectral matrix portraits
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 4, pp. 353-360.

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There exist classes of (in general) nonselfadjoint matrix operators whose eigenvalues of a spectral cluster are ill-conditioned. In applications, it is convenient to describe properties of such operators in terms of some criteria for spectral dichotomy. It is convenient to divide the spectrum by a series of plane curves depending on a single parameter. The graphical dependence of a criterion for dichotomy on this parameter is naturally regarded as spectral portrait. Criteria for dichotomy are connected with Hermite forms. (Recall that Hermite forms appeared in 1856 in solving a similar problem studied by Hermite). 
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S. K. Godunov. Partition of the spectrum by Hermite forms and one-dimensional spectral matrix portraits. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 4, pp. 353-360. http://geodesic.mathdoc.fr/item/SJVM_2001_4_4_a4/

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