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3 votes
1 answer
428 views

Minimum upper bound for sum of the entries of the inverse covariance matrix

Let $x \in \mathbb{R}^n$ and $k$ is RBF kernel $$k(x, x') := \exp \left(-\frac{\|x-x'\|^2}{2\sigma^2}\right)$$ and let $\mathbf{K}$ be the following $n \times n$ covariance matrix $$\mathbf{K} = \...
4 votes
2 answers
203 views

Results of invertibility of a matrix involving the Szego kernel

In the context of reproducing kernel Hilbert spaces, the Szego kernel is the function $k(z_i,z_j)=\frac{1}{1-z_j\overline{z_j}}$. Given $2n$ points $\{z_1,\ldots,z_n\},\{w_1,\ldots,w_n\}\in\mathbb{D}\...