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  "body": "\n## Summary\n\nThe Pick matrix of interpolation data $z_1, \\ldots, z_n$ in the [[unit disc|8G5ABXRK85]] and target values $w_1, \\ldots, w_n$ is the Hermitian matrix with entries $\\frac{1 - w_i \\overline{w_j}}{1 - z_i \\overline{z_j}}$.\nBy [[Nevanlinna–Pick interpolation|4VMSSYB5DN]], a holomorphic self-map of the disc with $f(z_i) = w_i$ exists exactly when this matrix is positive semidefinite.\nIt turns an analytic existence problem into a finite check of linear algebra.\n\n## Explanations\n\n### L1 human\n\nSuppose you want a holomorphic map of the disc into itself that sends some given points to some given values inside the disc.\nYou write down a square table of numbers built from the points and the values.\nIf that table is a [[positive semidefinite matrix|0880F9EQCP]], such a map exists; otherwise it does not.\nWith one point, the table is the single positive number $\\frac{1 - \\abs{w_1}^2}{1 - \\abs{z_1}^2}$, and indeed a [[Möbius transformation|0B346DDAM5]] of the disc sends $z_1$ to $w_1$.\n",
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