Abstract
In this manuscript, a generalized inverse eigenvalue problem is considered that involves a linear pencil (zJ[0,n]−H[0,n]) of (n+1) by (n+1) matrices arising in the theory of rational interpolation and biorthogonal rational functions. In addition to the reconstruction of the Hermitian matrix H[0,n], characterizations of the rational functions that are components of the prescribed eigenvectors are given. A condition concerning the positive-definiteness of J[0,n] which is often an assumption in the direct problem is also isolated. Further, the reconstruction of H[0,n] is viewed through the inverse of the pencil (zJ[0,n]−H[0,n]) which involves the concept of m-functions.
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