1.11.2 Tensor calculus

Problem: Given a symmetric tensor: \[ A_{i j}=\left(\begin{array}{ccc} 1 & 0 & 2 \\ 0 & -1 & 1 \\ 2 & 1 & 3 \end{array}\right) \text {. } \] Find: 1) Eigenvalues and eigenvectors of the tensor, 2) orts of the coordinate system associated with the principal axes of the tensor, 3) the rotation matrix to the principal axes of the tensor, 4) tensor invariants, 5) equation and type of the characteristic surface of the tensor and depict it.