Most of the applications of Principal Component Analysis (PCA) are non-geometric in their nature. However, there are also a few purely geometric applications. The focus of this book are the geometric properties of the PCA in the context of PCA bounding boxes and reflective symmetry. A frequently used heuristic for computing a bounding box of a set of points is based on PCA. Here, the quality of the PCA bounding boxes is investigated. Bounds on the worst case ratio of the volume of the PCA bounding box and the volume of the minimum volume bounding box are presented. Also, the impact of the...