S =
Box Aligned with Original Coordinate System Box Aligned with Eigenvectors Coordinate System

σ=[1.00001.00001.00001.00003.00001.00001.00001.00004.0000]\sigma = \begin{bmatrix}1.0000 && 1.0000 && 1.0000 \\ 1.0000 && 3.0000 && 1.0000 \\ 1.0000 && 1.0000 && 4.0000\end{bmatrix}

Eigenvalues (Principal Stresses) =[0.48592.42805.0861] = \begin{bmatrix}0.4859 \\ 2.4280 \\ 5.0861\end{bmatrix}

Normalized Eigenvectors (Principal Stress Directions) =[0.93650.30050.1810],[0.13980.79280.5932],[0.32170.53020.7844] = \begin{bmatrix}0.9365 \\ -0.3005 \\ -0.1810\end{bmatrix},\begin{bmatrix}0.1398 \\ 0.7928 \\ -0.5932\end{bmatrix},\begin{bmatrix}0.3217 \\ 0.5302 \\ 0.7844\end{bmatrix}

Q=[0.93650.30050.18100.13980.79280.59320.32170.53020.7844]Q = \begin{bmatrix}0.9365 && -0.3005 && -0.1810 \\ 0.1398 && 0.7928 && -0.5932 \\ 0.3217 && 0.5302 && 0.7844\end{bmatrix}

σ=[0.48590.00000.00000.00002.42800.00000.00000.00005.0861]\sigma' = \begin{bmatrix}0.4859 && 0.0000 && 0.0000 \\ 0.0000 && 2.4280 && -0.0000 \\ 0.0000 && -0.0000 && 5.0861\end{bmatrix}