Question: Problem 2 (20%) Let A c Rmxm be a symmetric matrix, with eigenvalues ordered as A, (A) 2 Az( A) . . . 2 Am(A).

Problem 2 (20%) Let A c Rmxm be a symmetric matrix, with eigenvalues ordered as A, (A) 2 Az( A) . . . 2 Am(A). Prove that M(A) = max TH(U'AU) VERmxk i=1 s.t. U' U = Ik, (1) for any ke {1, 2, .... m}

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