Perturbed spectra of defective matrices

[摘要] This paper is devoted to the perturbation theory for defectivematrices. We consider the asymptotic expansions of the perturbedspectrum when a matrixAis changed toA+tE, whereE≠0andt>0is a small parameter. In particular, we analyse the rationalexponents that may occur when the matrixEvaries over the sphere‖E‖ =ρ>0. We partially characterize the leading exponentsnoting that the description of the set of all leading exponentsremains an open problem.

[学科分类] 应用数学