On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems

Introduction. Let m be the number of degrees of freedom of a linear conservative dynamical systenm and let the point (q1, q2,9 * , q'Mn Pl p2, . . . p'mt) of the phase space be denoted by x = (xl, x2, , x.2M). A system of 2m ordinary differential equations of the first order, which are homogeneous, linear and do not contain t explicitly, is a canonical system if, and only if, there exists a symmetric matrix A, such that the differential equations may be written in the form (i) Bdx/dt =Ax,