Abstract Domain adaptation problems arise in a variety of applications, where a training dataset from the source domain and a test dataset from the target domain typically follow different distributions. The primary difficulty in designing effective learning models to solve such problems lies in how to bridge the gap between the source and target distributions. In this paper, we provide comprehensive analysis of feature learning algorithms used in conjunction with linear classifiers for domain adaptation. Our analysis shows that in order to achieve good adaptation performance, the second moments of the source domain distribution and target domain distribution should be similar. Based on our new analysis, a novel extremely easy feature learning algorithm for domain adaptation is proposed. Furthermore, our algorithm is extended by leveraging multiple layers, leading to a deep linear model. We evaluate the effectiveness of the proposed algorithms in terms of domain adaptation tasks on the Amazon review dataset and the spam dataset from the ECML/PKDD 2006 discovery challenge.