Symmetric 2×2 matrix functions with order preserving property

Abstract

It is known that the discrete matrix Riccati equation has the order preserving property under some assumptions. In this paper we formulate and prove the converse statement for the case when the dimensions of the matrices are \(2 \times 2\) and the order preserving property holds for all such symmetric matrices.

Keywords

• riccati matrix equation
• order preserving property
• symmetric matrix function