1. Let A be an m × d matrix, and let X = AAT(A transpose T) . Assume that X has d distinct, non-zero eigenvalues. Assume that m d. In order to find the eigendecomposition of X, we will need to find the eigendecomposition of an m × m matrix. Since m is much larger than d, this is slow. Give an algorithm for finding the eigenvectors and eigenvalues of X that only requires computing the eigendecomposition of a d × d matrix. You can use simple matrix operations and assume that you have an eigendecomposition black box subroutine, but avoid using the SVD as a black box.
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