During the past few years several interesting applications of eigenspace representation of images have been proposed. These include face recognition, video coding, and pose estimation. However, the vision research community has largely overlooked parallel developments in signal processing and numerical linear algebra concerning efficient eigenspace updating algorithms. These new developments are significant for two reasons: Adopting them will make some of the current vision algorithms more robust and efficient. More important is the fact that incremental updating of eigenspace representations will open up new and interesting research applications in vision such as active recognition and learning. The main objective of this paper is to put these in perspective and discuss a new updating scheme for low numerical rank matrices that can be shown to be numerically stable and fast. A comparison with a nonadaptive SVD scheme shows that our algorithm achieves accuracy levels for image reconstruction and recognition at a significantly lower computational cost. We also illustrate applications to adaptive view selection for 3D object representation from projections.