Strongly Cyclic Vectors

Systems of form $$y'(x) = A(x)y(x)$$ are considered, with matrix elements being truncated unknown infinite power series. The concept of a cyclic vector is generalized to the case of these systems by introducing the concept of a strongly cyclic vector. A method for checking the strong cyclicity of a vector is discussed. A sufficient condition that allows one to check the strong cyclicity of a vector by the form of the matrix of derivatives with respect to the system is derived.