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Deep learning has achieved excellent achievements and has become the mainstream in the field of aerial image classification. While obtaining remarkable success, deep learning-based approaches are notoriously dependent on large amounts of labelled data. Few-shot learning uses existing knowledge to learn from few samples and quickly generalizes to new tasks. In this work, we proposed the few-shot learning with deep economic network and teacher knowledge for aerial image classification. Firstly, we performed simplification twice to reduce large-scale parameters and computational effort in deep networks. In the first simplification, the redundancy in feature inputs' main components is reduced, and the implicit information in redundant components is extracted instead of directly discarding the redundant components. The channel and spatial redundancies in deeper layers' inputs are reduced in the second simplification. Secondly, the teacher knowledge guides the random sampling and uses limited samples to improve classification performance. We conducted extensive experiments on NWPU-RESISC45, RSD46-WHU, and UC Merced datasets. The experimental results reveal that the proposed method has better classification accuracy, fewer network parameters, and less computational effort. Experiments on miniImageNet, FC100, CUB, and cross-domain datasets show that our method also maintains advanced classification accuracy on few-shot image classification benchmarks. [ABSTRACT FROM AUTHOR]