Transformation from Real Homogeneous Systems of Degree L to Complex Homogeneous Systems of Degree (l, 0)

In eigenvalue analysis, transformation from real systems to complex systems is very important. First, we clarify a necessary and sufficient condition that solutions of real nonlinear systems coincide with solutions of transformed complex nonlinear systems in the real subspace. Moreover, we propose a complex transformation such that a) real homogeneous systems of degree with respect to r are transformed to complex homogeneous systems of degree ( , 0) with respect to r and b) solutions of real systems coincide with solutions of transformed complex systems in the real subspace. Then, we show examples.