Inter- and extrapolatory properties of matrix partial orderings

In this paper we study some matrix partial orderings with respect to the preserving the relation for original A or/and B and the linear combinations of A and B. The property that “between” (“above”, respectively) A and (“below”, respectively) B one can locate convex (affine) combinations of original matrices will be called interpolatory (extrapolatory, respectively). Besides “classical” orderings we introduce and discuss in the mentioned aspect the notion of f-orderings.