Given a system of two linear homogeneous first-order hyperbolic PDE's, $n_{\theta} + An_{\xi} = 0,$ I need to show the right eigenvectors of $A$ show in the direction of the characteristic lines. The PDE's being hyperbolic, A is diagonalizable ($A = R\Lambda R^{-1}$),thus one may write $m^i_{\theta} + \lambda_i m^i_{\xi} = 0,$ the characteristic lines being $\xi - \lambda_i\theta = const.$ Can somebody show the columns of R are parallel to the characteristic lines ?
↧