Hi, I have a semi-definite positive matrix A, and I power it with the Hadamard power, that is: A^3=A.*A.*A, where .* is the point-wise/Hadamard/Schur product. If I know the factorization of A, i.e. A=USV' (doing the SVD), can I say something about the factorization of A^k? I know there are some inequalities in the eigenvalues, but I was wondering if there exist a relation between the eigenvectors of A and A^k. Do you know any efficient way of finding a low dimensional factorization of A^k without explicitely computing A^k? Any information would be useful.
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