We address the feature extraction problem for document ranking in information retrieval. We then propose LifeRank, a Linear feature extraction algorithm for Ranking. In LifeRank, we regard each document collection for ranking as a matrix, referred to as the original matrix. We try to optimize a transformation matrix, so that a new matrix (dataset) can be generated as the product of the original matrix and a transformation matrix. The transformation matrix projects high-dimensional document vectors into lower dimensions. Theoretically, there could be very large transformation matrices, each leading to a new generated matrix. In LifeRank, we produce a transformation matrix so that the generated new matrix can match the learning to rank problem. Extensive experiments on benchmark datasets show the performance gains of LifeRank in comparison with state-of-the-art feature selection algorithms.