In this work, a novel approach is presented for the feature extraction step in hyperspectral image processing to form more discriminative features between different pixel regions. The proposed method combines both spatial and spectral information, which is very important for segmentation and classification of hyperspectral images. For comparison, five different feature sets are formed using eigen decomposition of local covariance matrices of subcubes located around a pixel of interest in the scene. Subcubes of neighbor pixels are obtained by a windowed structure to expose pattern similarities. As a novel approach, local covariance matrices are computed in eigenspace and proposed feature sets are created after this stage. Before the formation of feature sets in eigenspace, the original input space is transferred to eigenspace by linear and nonlinear manner by principal component analysis (PCA) and its kernelized version (KPCA) and they are used in the experiments comparatively. In the simulations, one hyperspectral scene with ground-truth and one without ground-truth are used for the segmentation and classification tasks. Results of experiments are evaluated with four different unsupervised learning algorithms for data without ground-truth and three different supervised learning algorithms for data with ground-truth comparatively.