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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper studies the estimation of the k-dimensional principal subspace of a population matrix based on sample covariance matrix. Two estimators based on convex and non-convex optimizations are developed for projection matrix with large or small magnitude entries, respectively. Both these two estimators are shown to enjoy satisfactory theoretical properties and experimental results compared with state-of-the-art estimators. It would be better to clearly explain what the oracle knowledge used in the proposed algorithm is, and how to set up the oracle estimator comparison experiments.