An elementary approach to the matricial Nevanlinna–Pick interpolation criterion

The matricial Nevanlinna–Pick interpolation criterion determines when there is an analytic matrix contraction valued function on the complex unit disc which assumes preassigned n × n matrix values w 1 ,…, w m at preassigned interpolation points z 1 ,…, z m . Taking ∥ w i ∥ i = 1,…, m , the necessary and sufficient condition is the positivity of the nm × nm matricial Pick matrix,