Interpolation by matrices

Abstract

Assume that two sets of k vectors in Rn are given, namely {x1,...,xk} and {y1,...,yk}, and a class of matrices, e.g., positive definite matrices, positive matrices, strictly totally positive matrices, or P-matrices. The question considered in this paper is that of determining necessary and sufficient conditions on these sets of vectors such that there exists an n x n matrix A in the given class satisfying Axj=yj (j= 1,...,k).