Inter- and extrapolatory properties of matrix partial orderings

In this paper we study some matrix partial orderings less than or equal to (?) with respect to the preserving the relation A less than or equal to (?) B for original A or/and B and the linear combinations of A and B. The prop erty that "between" ("above", respectively) A and ("below", respectively) B one can locate convex (affine) combinations of original matrices will be c alled interpolatory (extrapolatory, respectively). Besides "classical" orde rings we introduce and discuss in the mentioned aspect the notion off-order ings. (C) 2001 Elsevier Science Inc. All rights reserved.