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7
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Hölder continuity of spectrum of matrices
Endow $\mathbb{C}^{d \times d}$ with the norm induced by the Euclidean norm on $\mathbb{C}^d$. It is well-known (to those who know it well, I guess) that the spectrum $\sigma(A)$ of a matrix $A \in \...
4
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0
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A Toeplitz variant of the Hilbert matrix
It is well-known that the Hilbert matrix $H$, i.e., the symmetric Hankel matrix with entries
$$H_{m,n}=\frac{1}{m+n-1}, \quad m,n\in\mathbb{N},$$
determines a bounded operator on $\ell^{2}(\mathbb{N}...