The task of out-of-distribution (OOD) detection is crucial for deploying machine learning models in real-world settings. In this paper, we observe that the singular value distributions of the in-distribution (ID) and OOD features are quite different: the OOD feature matrix tends to have a larger dominant singular value than the ID feature, and the class predictions of OOD samples are largely determined by it. This observation motivates us to propose \texttt{RankFeat}, a simple yet effective \emph{post hoc} approach for OOD detection by removing the rank-1 matrix composed of the largest singular value and the associated singular vectors from the high-level feature. \texttt{RankFeat} achieves \emph{state-of-the-art} performance and reduces the average false positive rate (FPR95) by 17.90\% compared with the previous best method. The success of \texttt{RankFeat} motivates us to investigate whether a similar phenomenon would exist in the parameter matrices of neural networks. We thus propose \texttt{RankWeight} which removes the rank-1 weight from the parameter matrices of a single deep layer. Our \texttt{RankWeight}is also \emph{post hoc} and only requires computing the rank-1 matrix once. As a standalone approach, \texttt{RankWeight} has very competitive performance against other methods across various backbones. Moreover, \texttt{RankWeight} enjoys flexible compatibility with a wide range of OOD detection methods. The combination of \texttt{RankWeight} and \texttt{RankFeat} refreshes the new \emph{state-of-the-art} performance, achieving the FPR95 as low as 16.13\% on the ImageNet-1k benchmark. Extensive ablation studies and comprehensive theoretical analyses are presented to support the empirical results. Code is publicly available via \url{https://github.com/KingJamesSong/RankFeat}.