The eigenvectors are mutually orthogonal: $u_i \cdot u_j = 0$ for all $i \neq j$

The matrix $U = [u_1 \, u_2 \, u_3]$ is orthogonal: $U^T U = I$

$A = 2 u_1 u_1^T - 1 \cdot u_2 u_2^T + 4 u_3 u_3^T$ (spectral decomposition)

$A^T$ has the same eigenvalues and eigenvectors as $A$