Find out the eigenvalues and the normalized eigenvectors of an operator \( latex \hat{A} \), where A is given by \( latex A = \begin{bmatrix} 7 & 0 & 0 \\ 0 & 1 & -i \\ 0 & i & -1 \end{bmatrix} \).

Find out the eigenvalues and the normalized eigenvectors of an operator \( latex \hat{A} \), where A is given by \( latex A = \begin{bmatrix} 7 & 0 & 0 \\ 0 & 1 & -i \\ 0 & i & -1 \end{bmatrix} \).

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