Given two homogeneous rating matrices with some overlapped users/items whose mappings are unknown, this paper aims at answering two questions. First, can we identify the unknown mapping between the users and/or items? Second, can we further utilize the identified mappings to improve the quality of recommendation in either domain? Our solution integrates a latent space matching procedure and a refining process based on the optimization of prediction to identify the matching. Then, we further design a transfer-based method to improve the recommendation performance. Using both synthetic and real data, we have done extensive experiments given different real life scenarios to verify the effectiveness of our models. The code and other materials are available at http://www.csie.ntu.edu.tw/~r00922051/matching/