Pick matrix

In mathematics, a Pick matrix is a matrix which occurs in the study of interpolation problems for analytic functions.

It is defined as

:$P=left\; [frac\{u\_i^*\; u\_i\; -\; v\_j^*\; v\_j\}\{1-f\_i^*\; f\_j\}\; ight]\; ^\{n-1\}\_\{i,j=0\}$

where $(u\_i)$ and $(v\_i)$ are column vectors of dimension $p$ and $q$, respectively; and "z"* denotes the complex conjugate of "z". Here $f\_i$ are complex numbers inside the unit circle. That is,

: