Abstarct: Symplectic matrices play an important role in the analysis and numerical solution of matrix problems. Symplectic similarity transformations preserve the structures of Hamiltonian, skew Hamiltanian and symplectic matrices. baxsed on this fact symplectic matrices are used as the basic tool in the analysis and the numerical solution of Hamiltonian, skew Hamiltonian and symplectic eigenvalue problems. In this thesis several matrix factorizations related to symplectic matrices is provided and a singular value-like decomposition B = QDS