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In several applications of signal processing recursive algorithms for estimating a few eigenvectors of correlation or covariance matrices directly from the incoming samples are desirable. In this paper such algorithms are derived by starting from an extension of the classical power method of numerical analysis, instead of the usual gradient approach. This viewpoint leads to useful and relatively simple rules for determining the gain parameters of Owsley's stochastic gradient ascent algorithm for sensor array processing and Thompson's adaptive algorithm for unbiased frequency estimation using the Pisarenko method. A new, promising algorithm for adaptive estimation of eigenvectors corresponding to the smallest eigenvalues is introduced. Preliminary numerical results and comparisons are given, and a generalization of Thompson's algorithm for estimating several eigenvectors is represented.