On the Theory of the Matrix Riccati Equation

This paper is a continuation of the author's previous paper [1] with the same title, which contains an investigation of properties of the matrix Riccati equation with variable coefficients that arises from variational problems. For the investigation the matrix cross-ratio was introduced - an invariant of a quadruple of points in the Grassmann manifold of -dimensional subspaces in a -dimensional linear space with respect to the action of the unimodular group of generalized linear fractional transformations on the Grassmann manifold. The properties of the matrix cross-ratio are investigated in the present article; classes of complex Riccati equations giving rise to flows on homogeneous Siegel domains of types I, II, and III are distinguished; a matrix analogue of the Schwarzian derivative is introduced.Bibliography: 7 titles.