Opuscula Mathematica
Opuscula Math. 44, no. 6 (2024), 853-882

Symmetric 2×2 matrix functions with order preserving property

Viera Štoudková Růžičková
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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About the authors ▼
Viera Štoudková Růžičková
https://orcid.org/0000-0001-5493-7630
Brno University of Technology, Institute of Mathematics, Faculty of Mechanical Engineering, Brno, Czech Republic
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2024-04-18.
Accepted: 2024-07-07.
Published online: 2024-10-11.
Cite this article as ▼
Viera Štoudková Růžičková, Symmetric 2×2 matrix functions with order preserving property, Opuscula Math. 44, no. 6 (2024), 853-882, https://doi.org/10.7494/OpMath.2024.44.6.853.
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