On similarities of class Cp and applications to matrix differential equations

AbstractThis paper deals with similarities of class Cp, in particular reduction of class Cp to Jordan form and unitary triangularization of class Cp of a matrix function. The main result is applied to establish a method to lower the order of nonlinear matrix differential equations belonging to a broad class of equations. In particular, this method permits one to transform nonlinear equations of the first order into an algebraic equation joint to a linear differential equation of the first order. The method is applied to the matrix differential equation XX′ − X′X = X, and a particular solution is easily obtained