Linear Discriminant Analysis(LDA) is widely-used in face recognition systems. However, with the traditional formulation, the available information in the training samples is not sufficiently utilized. In this paper, we present a new formulation, called Generalized LDA, where the scatter matrices are defined in a more flexible manner by identifying the fundamental principles of the scatter matrices construction. We further propose a novel framework called Feedback-based Dynamic Generalized LDA. It integrates the Generalized LDA and the dynamic feedback strategy for subspace analysis, in which the subspace is iteratively optimized by utilizing the feedback from the previous step. The comparative experiments demonstrate that the new framework achieves encouraging improvement on performances of both the face identification and the face verification.