Symmetric/skew-symmetric homogeneous matrix descriptor (regular) differential systems with consistent initial conditions

This paper introduces the results of Thompson´s canonical form under congruence for pairs of complex matrices with symmetric and skew symmetric structural properties to the solution of higher order linear matrix homogeneous differential systems. Under this approach, the main equation is divided into five sub-systems whose solutions are derived. Note that the regularity or singularity of matrix pencil predetermines the number of sub-systems. The special properties of such systems may be appeared in engineering and even in some financial models.