Recently, Discriminative Correlation Filters (DCF) have achieved enormous popularity in the tracking community due to high efficiency and fair robustness. With the circular structure, DCF transform computationally consuming spatial correlation into efficient element-wise operation in the Fourier domain. In this paper, we argue that this element-wise solution can be derived only in the case of single-channel features. In terms of tracking with multi-channel features, this element-wise solution trains each feature dimension independently and fails to learn a joint correlation filter. To tackle this problem, we propose a rigorous solution to closed-form correlation filter tracking. This rigorous solution can be computed pixel by pixel from a small linear equation system. Experimental results demonstrate that our rigorous pixel-wise solution achieves better tracking performance than the baseline element-wise solution.