Pick matrix

Summary

The Pick matrix of interpolation data $z_1, \ldots, z_n$ in the unit disc and target values $w_1, \ldots, w_n$ is the Hermitian matrix with entries $\frac{1 - w_i \overline{w_j}}{1 - z_i \overline{z_j}}$. By Nevanlinna–Pick interpolation, a holomorphic self-map of the disc with $f(z_i) = w_i$ exists exactly when this matrix is positive semidefinite. It turns an analytic existence problem into a finite check of linear algebra.