I am stuck trying to solve the following problem:
In diagonalizing a symmetric matrix $S$, we find that two of the eigenvalues ($\lambda_1$ and $\lambda_2$) are equal but the third ($\lambda_3$) is different. Show that any vector which is normal to $\hat{n}_3$ (which is the eigenvector corresponding to $\lambda_3$) is then an eigenvector of $S$ with eigenvalue equal to $\lambda_1$
Can anyone offer hints on, or an outline of, the solution?
Thank you.