TY - GEN A1 - Mehl, Christian A1 - Mehrmann, Volker A1 - Ran, Andre A1 - Rodman, Leiba T1 - Perturbation theory of selfadjoint matrices and sign characteristics under generic structured rank one perturbations N2 - For selfadjoint matrices in an indefinite inner product, possible canonical forms are identified that arise when the matrix is subjected to a selfadjoint generic rank one perturbation. Genericity is understood in the sense of algebraic geometry. Special attention is paid to the perturbation behavior of the sign characteristic. Typically, under such a perturbation, for every given eigenvalue, the largest Jordan block of the eigenvalue is destroyed and (in case the eigenvalue is real) all other Jordan blocks keep their sign characteristic. The new eigenvalues, i.e., those eigenvalues of the perturbed matrix that are not eigenvalues of the original matrix, are typically simple, and in some cases information is provided about their sign characteristic (if the new eigenvalue is real). The main results are proved by using the well known canonical forms of selfadjoint matrices in an indefinite inner product, a version of the Brunovsky canonical form and on general results concerning rank one perturbations. KW - indefinite inner product KW - selfadjoint matrices KW - perturbation analysis KW - generic perturbation KW - rank one perturbation Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/671 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6710 ER -