Matrix Differential Equations for Pseudo-orthogonal Groups

Abstract

We consider a system of matrix differential equations whose nondegenerate solutions are O(n, p, R)-equivalent, where O(n, p, R) is the pseudo-orthogonal group of invertible linear transformations of \(R^n\). We show that the class of first columns of the set of matrices that are nondegenerate solutions of this system coincides with the class of O(n, p, R)-equivalent paths in \(R^n\).