Orthogonality of Eigenvectors of a Symmetric Matrix Corresponding to Distinct Eigenvalues
Problem 235
Suppose that a real symmetric matrix $A$ has two distinct eigenvalues $\alpha$ and $\beta$.
Show that any eigenvector corresponding to $\alpha$ is orthogonal to any eigenvector corresponding to $\beta$.
(Nagoya University, Linear Algebra Final Exam Problem)
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