Few-shot object detection (FSOD) aims to detect new objects based on few annotated samples. To alleviate the impact of few samples, enhancing the generalization and discrimination abilities of detectors on new objects plays an important role. In this paper, we explore employing Singular Value Decomposition (SVD) to boost both the generalization and discrimination abilities. In specific, we propose a novel method, namely, SVD-Dictionary enhancement, to build two separated spaces based on the sorted singular values. Concretely, the eigenvectors corresponding to larger singular values are used to build the generalization space in which localization is performed, as these eigenvectors generally suppress certain variations (e.g., the variation of styles) and contain intrinsical characteristics of objects. Meanwhile, since the eigenvectors corresponding to relatively smaller singular values may contain richer category-related information, we can utilize them to build the discrimination space in which classification is performed. Dictionary learning is further leveraged to capture high-level discriminative information from the discrimination space, which is beneficial for improving detection accuracy. In the experiments, we separately verify the effectiveness of our method on PASCAL VOC and COCO benchmarks. Particularly, for the 2-shot case in VOC split1, our method significantly outperforms the baseline by 6.2\%. Moreover, visualization analysis shows that our method is instrumental in doing FSOD.