Let be the identity matrix, and let . The matrix is called symplectic if holds, and the system , , is symplectic if the matrix is symplectic. A solution to the system has a generalized zero in if , and , where denotes the Moore-Penrose inverse of the matrix . The system is called disconjugate on if no solution of the system has more than one generalized zero (if no zero).
Theorem 1 shows a lot of equivalent facts about disconjugacy, possession of generalized zeros and other similar properties of the solution to the symplectic system. Similar results are obtained relative to the reciprocal symplectic system . The problems of eventually disconjugate solutions and disconjugacy preserving transformations are considered as well.