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A method is presented for rapidly estimating the principal components used in dimension reduction for high frame rate hyperspectral video systems. Pixels entering and leaving a video frame are used to rapidly update the covariance matrix (Σ) and estimate the perturbed eigenpairs. Measuring the angle between the estimated dominant eigenspace and the exact eigenspace shows the method to be a good approximation when the difference between frames is low (||δΣ|| ≪ ||Σ||). This method reduces the time to calculate the principal components of high resolution hyperspectral video data by a factor of ~20.