Recently, the advances in passive brain-computer interfaces (BCIs) based on electroencephalogram (EEG) have shed light on real-world neuromonitoring technologies. However, human variability in the EEG activities hinders the development of practical applications of EEG-based BCI. To tackle this problem, many transfer-learning techniques perform supervised calibration. This kind of calibration approach requires task-relevant data, which is impractical in real-life scenarios such as drowsiness during driving. This study presents a transfer-learning framework for EEG decoding based on the low-dimensional representations of subjects learned from the pre-trial EEG. Tensor decomposition was applied to the pre-trial EEG of subjects to extract the underlying characteristics in subject, spatial and spectral domains. Then, the proposed framework assessed the characteristics to obtain the low-dimensional subject representations such that the subjects with similar brain dynamics can be identified. This method can leverage the existing data from other users and a small number of data from a rapid, non-task, unsupervised calibration from a new user to build an accurate BCI. Our results demonstrated that, in terms of prediction accuracy, the proposed low-dimensional subject representation-based transfer learning (LDSR-TL) framework outperformed the random selection and the Riemannian manifold approach in cognitive-state tracking, while requiring fewer training data. The results can greatly improve the practicability and usability of EEG-based BCI in the real world.