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eigenvalues of matrices or operators

1 vote
2 answers
427 views

Is Rellich's function valued theorem valid for a rank defficient function valued matrix?

My question is what happens if some of the eigenvalues have multiplicity,i.e. $\lambda_j(t)=\lambda_k(t)$ for some values of $t$ if $k\neq j$. …
0 votes
1 answer
102 views

The influence of eigendecomposition on the periodicity of a (rank 2) Hermitian matrix (of fu...

Let $\boldsymbol{R}(u,v);~u,v\in\mathbb{R}$ be a Hermitian matrix (of Hermitian functions) with entries \begin{equation} r_{ij}(u,v) = 1 + Ae^{-2\pi i \phi_{ij}(ul_0 + vm_0)}; A\in\mathbb{R},l_0\in\ma …