Discrete Riccati matrix equation and the order preserving property

Abstract

It is known that if a symmetric matrix differential equation has the order preserving property and the matrix dimension is at least 2, then this equation is the Riccati matrix differential equation (see [20]). In this paper we prove that a similar statement holds for discrete matrix equations as well. In the proof we use a new approach, in which we extend a discrete function to a continuous one by using the iteration theory and then apply the known result for the continuous case.