Opuscula Math. 44, no. 6 (2024), 853-882
https://doi.org/10.7494/OpMath.2024.44.6.853
Opuscula Mathematica
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.
Mathematics Subject Classification: 39A12, 39A22, 26B35.
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- Viera Štoudková Růžičková
https://orcid.org/0000-0001-5493-7630- Brno University of Technology, Institute of Mathematics, Faculty of Mechanical Engineering, Brno, Czech Republic
- Communicated by P.A. Cojuhari.
- Received: 2024-04-18.
- Accepted: 2024-07-07.
- Published online: 2024-10-11.
