ELA, Volume 11, pp. 281-291, November 2004, abstract.
Interpolation by Matrices
Allan Pinkus
Assume that two sets of k vectors in R^n are
given, namely {x^1,...,x^k} and {y^1,...,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 nxn matrix A in the given class satisfying
Ax^j = y^j (j=1,...,k).