Pick matrix
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In mathematics, a Pick matrix is a matrix (mathematics) which occurs in the study of interpolation problems, for analytic functions.
It is defined as
- <math>P=\left[\frac{u_i^* u_i - v_j^* v_j}{1-f_i^* f_j}\right]^{n-1}_{i,j=0}<math>
where <math>(u_i)<math> and <math>(v_i)<math> are column vectors of dimension <math>p<math> and <math>q<math>, respectively; and z* denotes the complex conjugate of z. Here <math>f_i<math> are complex numbers inside the unit circle. That is,
- <math>|f_i|<1<math>.