Regularity of systems of linear differential equations of block-triangle form (Q1097386)

The author assumes the existence of two bounded continuously differentiable symmetric matrix functions such that the derivative of the quadratic forms defined by these matrices along the trajectories of the dual system is sign-defined. He proves that the regularity (or pseudoregularity) of the original system depends on the number of positive eigenvalues of a block-diagonal matrix constructed from the above-mentioned matrices.