Person re-identification is an important technique towards automatic search of a person's presence in a surveillance video. Among various methods developed for person re-identification, the Mahalanobis metric learning approaches have attracted much attention due to their impressive performance. In practice, many previous papers have applied the Principle Component Analysis (PCA) for dimension reduction before metric learning. However, this may not be the optimal way for metric learning in low dimensional space. In this paper, we propose to jointly learn the discriminant low dimensional subspace and the distance metric. This is achieved by learning a projection matrix and a Restricted Quadratic Discriminant Analysis (RQDA) model. We show that the problem can be formulated as a Generalized Rayleigh Quotient, and a closed-form solution can be obtained by the generalized eigenvalue decomposition. We also present a practical computation method for RQDA, as well as its regularization. For the application of person re-identification, we propose a Retinex and maximum occurrence based feature representation method, which is robust to both illumination and viewpoint changes. Experiments on two challenging public databases, VIPeR and QMUL GRID, show that the performance of the proposed method is comparable to the state of the art.