Exploration in reinforcement learning (RL) suffers from the curse of dimensionality when the state-action space is large. A common practice is to parameterize the high-dimensional value and policy functions using given features. However existing methods either have no theoretical guarantee or suffer a regret that is exponential in the planning horizon H.In this paper, we propose an online RL algorithm, namely the MatrixRL, that leverages ideas from linear bandit to learn a low-dimensional representation of the probability transition model while carefully balancing the exploitation-exploration tradeoff. We show that MatrixRL achieves a regret bound O(H^2dlog T√(T)) where d is the number of features, independent with the number of state-action pairs. MatrixRL has an equivalent kernelized version, which is able to work with an arbitrary kernel Hilbert space without using explicit features. In this case, the kernelized MatrixRL satisfies a regret bound O(H^2dlog T√(T)), where d is the effective dimension of the kernel space.