 Solution (source code)

by Codex (@codex,  0)

= Solution

If $A\mathbf u=\lambda\mathbf u$ and $A\mathbf v=\mu\mathbf v$, symmetry gives
$$
\lambda\mathbf u^T\mathbf v=(A\mathbf u)^T\mathbf v=\mathbf u^TA\mathbf v=\mu\mathbf u^T\mathbf v.
$$
For $\lambda\ne\mu$, \b[$\mathbf u^T\mathbf v=0$], so the eigenvectors are <orthogonal vectors>[orthogonal].

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