Spectral singularities and self-orthogonality of eigenvectors


Spectral singularities and self-orthogonality of eigenvectors

Günther, U.; Graefe, E.-M.; Korsch, H.-J.; Niederle, A.; Rotter, I.; Samsonov, B.

A brief overview of some mathematical aspects connected with the occurrence of spectral singularities will be presented. Based on simple matrix models we discuss stratified manifolds in parameter spaces on which the matrix eigenvalues degenerate. We comment on discriminant sets and similarity relations to canonical Jordan structures, demonstrate the mechanism underlying the formation of self-orthogonal (isotropic) eigenvectors, relate it to corresponding projectors. Special emphasis will be laid on the break-down of similarity transformations, the formation of corresponding transformation singularities and their resolution via projective extensions. Structural links to ultrarelativistic spinor models will be sketched. Finally, we comment on versal deformations and an unfolding rule for higher-order spectral singularities connected with the Hessenberg type of the perturbation.

Keywords: spectral; singularity; Jordan structure; exceptional point; self-orthogonality; isotropy; versal deformation; projective extension; ultra-relativistic limit; Hessenberg matrix

  • Invited lecture (Conferences)
    Experimental Realizations of Self-Orthogonality, 23.-28.03.2008, Haifa, Israel

Permalink: https://www.hzdr.de/publications/Publ-11058
Publ.-Id: 11058