1 and \nlimk~oo sup(l7i l -l7i~l) <00. \nAssumption (A3). The p largest generalized eigenvalues of A with respect to B are each \nof unit mUltiplicity. \nLemma 1. Let Al and A2 hold. Let w* be a locally asymptotically stable (in the sense of \nLiapunov) solution to the ordinary differential equation (ODE): \n\n\fSelf-Organizing and Adaptive Generalized Eigen-Decomposition \n\n~ W(t) = 2AW(t) - BW(t)U4W(t/ AW(t)] - AW(t)U4W(t/ BW(t)], \n\n401 \n\n(11) \n\nwith domain of attraction D(W). Then if there is a compact subset S of D(W) such that \nWk E S infinitely often, then we have Wk ~ W with probability one as k ~ 00. \nWe denote A\\ > ~ > ... > Ap ~ ... ~ An > 0 as the generalized eigenvalues of A with \nrespect to B, and 4>; as the generalized eigenvector corresponding to A; such that 4>\\, ... ,4>n \nare orthonormal with respect to B. Let