Question: Prove that, if A is a symmetric matrix with eigenvalues 1, 2,..., n, then the singular values of A are |1|, |2|,..., |n|.

Prove that, if A is a symmetric matrix with eigenvalues λ1, λ2,..., λn, then the singular values of A are |λ1|, |λ2|,..., |λn|.

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