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The need to generate new views of a 3D object from a single real image arises in several fields, including graphics and object recognition. While the traditional approach relies on the use of 3D models, simpler techniques are applicable under restricted conditions. The approach exploits image transformations that are specific to the relevant object class, and learnable from example views of other "prototypical" objects of the same class. In this paper, we introduce such a technique by extending the notion of linear class proposed by the authors (1992). For linear object classes, it is shown that linear transformations can be learned exactly from a basis set of 2D prototypical views. We demonstrate the approach on artificial objects and then show preliminary evidence that the technique can effectively "rotate" high-resolution face images from a single 2D view.