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In the study of the Sparre Andersen risk model with phase-type inter-claim times, the roots in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundbergs matrix play important roles.In this paper, we show that, for the phase-type(2) inter-claim times, the roots with positive real parts of the Lundbergs fundamental equation are distinct and the corresponding eigenvectors are linearly independent.