The height of an nth-order fundamental rogue wave for the nonlinear Schrödinger equation

The height of an nth-order fundamental rogue wave qrw[n] for the nonlinear Schrödinger equation, namely (2n+1)c, is proved directly by a series of row operations on matrices appeared in the n-fold Darboux transformation. Here the positive constant c denotes the height of the asymptotical plane of the rogue wave.