Example of Spectral Theorem (3x3 Symmetric Matrix)

Linear Algebra:  We verify the Spectral Theorem for the 3x3 real symmetric matrix A = [ 0 1 1 / 1 0 1 / 1 1 0 ].   That is, we show that the eigenvalues of A are real and that there exists an orthonormal basis of eigenvectors. In other words, we can put A in real diagonal form using an orthogonal matrix P.  (Eigenvalues and eigenvectors for this A are found in the video "Eigenvalues and Eigenvectors.")

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