Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • University of Oxford

Kuvaus

Sylvester's law of inertia states that the number of positive, negative and zero eigenvalues of Hermitian matrices is preserved under congruence transformations. The same is true of generalized Hermitian definite eigenvalue problems, in which the two matrices are allowed to undergo different congruence transformations, but not for the indefinite case. In this paper we investigate the possible change in inertia under congruence for generalized Hermitian indefinite eigenproblems, and derive sharp bounds that show the inertia of the two individual matrices often still provides useful information about the eigenvalues of the pencil, especially when one of the matrices is almost definite. A prominent application of the original Sylvester's law is in finding the number of eigenvalues in an interval. Our results can be used for estimating the number of real eigenvalues in an interval for generalized indefinite and nonlinear eigenvalue problems.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut272-296
Sivumäärä25
JulkaisuLinear Algebra and Its Applications
Vuosikerta578
TilaJulkaistu - 1 lokakuuta 2019
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 36262303