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In this note, we have proposed a prediction error based adaptive Jacobian controller to solve the problem of concurrent adaptation to both uncertain kinematics and dynamics. This controller is composed of a modified computed torque controller and two cushion floor least-square estimators, and in ideal case of perfect knowledge of the robot parameters it leads to linear and decoupled error dynamics. The kinematic and dynamic parameters adaptations are driven by prediction errors. Using input-output stability analysis, we show that the end-effector motion tracking errors converge asymptotically. We have also derived an alternative adaptive Jacobian controller that does not require the invertibility of the estimated inertia matrix. Simulation results are presented to show the performance of the proposed controllers.