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 $\{z_1,\ldots,z_n\},\{w_1,\ldots,w_n\}\in\mathbb{D}\cap\mathbb{R}$, (with all $z_i$'s different and all $w_i$'s different, but the sets may not be disjoint), are there any known result of the invertibility of the matrix: $$\big[k(z_i,w_j)]_{i,j=1}^n$$

For all sets of $4$ points I have tested, this matrix came out invertible. I wasn't able, however, to determine if it is always the case. Moreover, I didn't find any information on whether there are conditions on the sets of points for which this matrix is indeed invertible.

Any help would be greatly appreciated.