Shot boundary detection is the first step of the video analysis, summarization and retrieval. In this paper, we propose a novel shot boundary detection algorithm using Generalized Eigenvalue Decomposition (GED) and modeling of gradual transitions by Gaussian functions. Especially, we focus on the challenges of detecting the gradual shots and extracting appropriate spatio-temporal features, which have effects on the ability of algorithm to detect shot boundaries efficiently. We derive a theorem that discuss about some new features of GED which could be used in the video processing algorithms. Our innovative explanation utilizes this theorem in the defining of new distance metric in Eigen space for comparing video frames. The distance function has abrupt changes in hard cut transitions and semi-Gaussian behavior in gradual transitions. The algorithm detects the transitions by analyzing this distance function. Finally we report the experimental results using large-scale test sets provided by the TRECVID 2006 which has evaluations for hard cut and gradual shot boundary detection.