Adjoint matrix differential systems
This paper is devoted to a specific subject of the projective theory of matrix differential systems, namely the adjoint systems. An adjoint equation is first defined after a ``Lagrange identity'' has been derived. Lagrange identity is the fundamental coupling which corresponds to the coupling between a system of vector differential equations and its adjoint in the classical theory. The geometric relation between the initial equation and its adjoint is then considered. Finally, the notion of self adjoint equations is defined and ``singular'' equations (for which the matrix coefficient of the highest order derivative is not invertible) are considered. Related references are recent works by the author and A. Zaks, as well as a book by \textit{E. J. Wylczynski} [first edition (1906)] for the relations with projective theory.
projective theory of matrix differential systems
scientific article; zbMATH DE number 4105368