Find the spectral decomposition of the \mathbf{S}. That is, find the eigenvalues and their corresponding eigenvectors.
Enter the eigenvalues in decreasing order (so \lambda _1>\lambda _2.)
\lambda ^{(1)}=\quad
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\lambda ^{(2)}=\quad
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Find the eigenvectors \mathbf v_{\lambda _1} and \mathbf v_{\lambda _2}. (All scalar multiples will be accepted)
\mathbf v_{\lambda _1}=\quad
\mathbf v_{\lambda _2}=\quad
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I'm sorry, but you haven't provided a matrix \mathbf{S}. Without the matrix, I cannot calculate the eigenvalues and eigenvectors. Please provide the matrix \mathbf{S}, and I will be happy to help you with the spectral decomposition.
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