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V. Derevenskii (2017)
Differential equations over subalgebras of the full matrix algebraDifferential Equations, 53
V. Derevenskii (2014)
Quadratic equations over matrix skew seriesRussian Mathematics, 58
V. Derevenskii (1994)
Matrix two-sided linear differential equationsMathematical Notes, 55
The notions of semilalgebra and its associated subalgebra are introduced. Linear spaces ofrow-column, skew-angle, and acute-angle matrices that are subalgebras or semialgebras of the fullmatrix algebra are also defined. Conditions for the splittability and solvability by quadratures of amatrix linear ordinary differential equation of the first order with two-sided multiplication\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$dX/dt=\sum_{k=1}^K A_k X B_k+C$$\end{document} are studied, where\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$K\in \mathbb {N}$$\end{document} and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$X$$\end{document} and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A_k$$\end{document}, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_k$$\end{document}, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C$$\end{document} are, respectively, the unknown and givenmatrix-valued continuously differentiable functions of the variable \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t\in \mathbb {R}$$\end{document} ranging in one of these linear spaces.
Differential Equations – Springer Journals
Published: Jun 5, 2020
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