Symmetric 2x2 matrix functions with order preserving property

• Autorzy: Růžičková Viera Štoudková

Identyfikatory

DOI

10.7494/OpMath.2024.44.6.853

• Języki publikacji: EN

Abstrakty

EN

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 × 2 and the order preserving property holds for all such symmetric matrices.

Słowa kluczowe

EN

Riccati matrix equation; order preserving property; symmetric matrix function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 6
• Strony: 853--882
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Růžičková Viera Štoudková

• Brno University of Technology, Institute of Mathematics, Faculty of Mechanical Engineering, Brno, Czech Republic

• https://orcid.org/0000-0001-5493-7630

Bibliografia

• [1] W.A. Coppel, Disconjugacy, Lecture Notes in Mathematics, vol. 220, Springer-Verlag, Berlin–New York, 1971.
• [2] N.J. Higham, Functions of Matrices, Theory and Computation, SIAM, Philadelphia, 2008.
• [3] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177–216.
• [4] W.T. Reid, Riccati Differential Equations, Mathematics in Science and Engineering, vol. 86, Academic Press, New York–London, 1972.
• [5] R. Šimon Hilscher, Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems, Electron. J. Qual. Theory Differ. Equ. 2015, no. 54, 1–16.
• [6] A.N. Stokes, A special property of the matrix Riccati equation, Bull. Austral. Math. Soc. 10 (1974), 245–253.
• [7] V. Štoudková Růžičková, Discrete Riccati matrix equation and the order preserving property, Linear Algebra Appl. 618 (2021), 58–75.
• [8] V. Štoudková Růžičková, Riccati matrix differential equation and the discrete order preserving property, Arch. Math. (Brno) 59 (2023), no. 1, 125–131.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)