Partition of Real Symmetric Matrices According to the Multiplicities of TheirEigenvalues

摘要

In this paper we will be concerned with a partition of the set of all realsymmetric n x n-matrices into strata corresponding to the multiplicities of the eigenvalues. It will be shown that this stratification is Whitney Regular. Moreover, we derive an explicit formula for the codimension of the strata in terms of the multiplicities involved. The transversality theory of R. Thom leads to generic perturbation results for the eigenvalues of one-parameter families of real symmetric matrices. The connections with sensitivity results in parametric optimization are investigated.