I have a symmetric matrix A, whose eigenvalues are $\lambda_1 = 6,~ \lambda_2 = 3,~ \lambda_3 = 2$ and eigenvectors are $\vec{v_1} = (1, 1, 1),~\vec{v_2} = (1,1,-1)$. How do I find the third eigenvector $\vec{v_3}$?
2026-03-26 18:49:56.1774550996
How do I find this eigenvector for a symmetric Matrix?
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Hint: Since the matrix is symmetric, (and real, I presume) it has an orthogonal basis of eigenvectors.