Hermitian matrices depending on three parameters: Coalescing eigenvalues
The behavior of eigenvalues under perturbation is a classical problem. Eigenvalues of a matrix valued functions can always be chosen as continuous functions of the parameters, but further smoothness is generally precluded multiple eigenvalues are encountered. However, severe lack of smoothness can be expected whenever there are multiple eigenvalues. The authors study what happens when one or more eigenvalues of a matrix depending on parameters come together (coalescing eigenvalues) for Hermitian matrix valued functions depending on three parameters that vary in a bounded surface of \({\mathbb R}^3\). They are interested in giving global, hence topological, localization results for values in parameter space where the eigenvalues coalesce, and their particular emphasis is on Hermitian matrices depending on three parameters. Some pictures are helpful on idea illustration.
scientific article; zbMATH DE number 6033310
scientific article