<p>Principal component analysis (PCA) is ubiquitous in statistics and machine learning domains. It is frequently used as an intermediate procedure in various regression and classification problems to reduce the dimensionality of datasets. However, as the size of datasets becomes extremely large, direct application of PCA may not be feasible since loading and storing massive datasets may exceed the computational ability of common machines. To address this problem, subsampling is usually performed, in which a small proportion of the data is used as a surrogate of the entire dataset. This paper proposes an A-optimal subsampling algorithm to decrease the computational cost of PCA for super-large datasets. To be more specific, we establish the consistency and asymptotic normality of the eigenvectors of the subsampled covariance matrix. Subsequently, we derive the optimal subsampling probabilities for PCA based on the A-optimality criterion. We validate the theoretical results by conducting extensive simulation studies. Moreover, the proposed subsampling algorithm for PCA is embedded into a classification procedure for handwriting data to assess its effectiveness in real-world applications.</p>