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    Let A be a (m x m) Normal Matrix

    a) Calculate the singular values of A as a function of the eigenvalutes of A.
    b) Prove that the eigenvalues of A are all purely imaginary if and only if A is anti-symmetric (A^H = -A)

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    Solution Preview

    (a) The spectral theorem can be applied to obtain unitary diagonalization of A = UΛU * . Therefore,

    sqrt{A*A} = U |Λ| U*

    and so the singular values are simply the absolute values of the ...

    Solution Summary

    The expert calculate the singular values in this case.The eigenvalues of A are all proved.