Generalizations of Oja's Learning Rule to Non-Symmetric Matrices

New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja's and Xu's principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.

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