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Invariants:

S = Stress Tensor \begin{pmatrix} \sigma_{11}&\sigma_{12}&\sigma_{13}\\\sigma_{21}&\sigma_{22}&\sigma_{23}\\\sigma_{31}&\sigma_{32}&\sigma_{33}\\ \end{pmatrix}

with its associated eigenvalues: \lambda_1 , \lambda_2 , \lambda_3 , \lambda_i \epsilon\mathbb{R},i=1,2,3

*Eigen Values are all real because Tensor is symetric

S’ = Diagonalized Stress Tensor = \begin{pmatrix} \lambda_{1}&0&0\\0&\lambda_{2}&0\\0&0&\lambda_{3}\\ \end{pmatrix}

I1(S)=Trace(S) =I1(S')=\lambda_1+\lambda_2+\lambda_3 I2(S)=\lambda_1*\lambda_2+\lambda_2*\lambda_3+\lambda_3*\lambda_3 I3(S) =I3(S')=\lambda_1*\lambda_2*\lambda_3