Question: For a square symmetric matrix, we call eigen decomposition the collection of all its eigenvector-eigenvalue pairs. Let A R n*n be a square symmetric matrix.

For a square symmetric matrix, we call eigen decomposition the collection of all its eigenvector-eigenvalue pairs. Let A R^n*n be a square symmetric matrix. Give the eigen decomposition of A^k as a function of the eigen decomposition of A for any integer k > 0.

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