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Local differentiability of eigenvalues and eigenvectors of a real symmetric matrix

Let $A(x)\in\mathbb{R}^{n\times n}$ be a real symmetric matrix depending on the point $x\in\mathbb{R}^n$, where the eigenvalues are not necessarily simple. Can we say that for all $x$ there exists an ...
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On generalization of Wigner semi circle

I want to analyse noise model for a matrix M whose entries are not real numbers. The matrix is a collection of N permutation matrices of size nxn i.e, M is NnxNn. Because its a collection of ...