Let P be a symmetric positiove definite Pick matrix of order n. The following facts will be proven here: 1. P is the Gram matrix of a set of rational funtions, with respect to a inner product defined in terms of a "generating function" associated to P; 2. Its condition number is lower-boudned by a function growing exponentially in n. 3. P can be effectively preconditioned by the Pick matrix generated by the same nodes and a constant function.
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