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).