Hyperspectral systems have significantly progressed through recent advancements in sensor technology, which have made it possible to collect data with several hundred channels. While these remote sensing technology developments hold great promise for new findings in the areas of Earth and space science, they also present many challenges. These include the need for methods of data reduction, and faster processing of such increased data volumes. Principal Component Analysis (PCA) is one such data reduction technique, which is often used when analyzing remotely sensed data. For example, with land cover classification, most conventional methods require the preprocessing step of dimension reduction, which can be seen as a transformation from a high order dimension to a low order dimension to conquer the so-called curse of the dimensionality. Scientists typically produce all principal components (PCs) and then select from among them those that have significant information, which could be error prone. Using the so-called power method, the algorithm finds the eigenvalues one by one, starting from the largest and stopping when a predetermined threshold is reached. This threshold represents the desired amount of information content that corresponds to the computed eigenvalues as a percentage of the overall information content of the image. It will be shown that the algorithm presented in this paper can select accurately and compute only the needed PCs in an automatic fashion. It will be also shown that this algorithm is far more computationally efficient than existing methods.