Interpolation by matrices

Abstract

Assume that two sets of k vectors in Rⁿ are given, namely {x¹,...,x^k} and {y¹,...,y^k}, 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 Ax^j=y^j (j= 1,...,k).