Tensor compact/matrix form.

326 Views Asked by At

I have got this tensor $S_{ij} = \frac{1}{2}(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i})$

Anyway I solve it for my problem and get

$$ S_{ij} = \left( \begin{array}{ccc} 0 & b1 & 0 \\ b1 & 0 & b3 \\ 0 & b3 & 0 \end{array} \right) $$

The question is why when I put it back in compact form and perform $ 2(S_{ij} S_{ij})$ the following is obtained?

$$ 2(S_{ij} S_{ij}) = b1^2 + b3^2 $$

I don't how to put it back in compact form.

Thanks for your help, Fred