# Form the 4th dimensional 2nd order T to find its determinant and eigenvalues.

A 4th dimensional 2nd order tensor is given as $$\overline {\overline T}=2\vec e_1\vec f_1+2\vec e_2\vec f_2+\vec e_1\vec f_2+\vec e_2\vec f_1+\epsilon:\vec e_1\vec e_2$$ where $$\vec e_i.\vec f_j=\delta_{ij}$$ and $$\epsilon$$ is 4-D permutation tensor. Also $$\vec f_3=2\vec e_3-\vec e_4$$ and $$\vec f_4=\vec e_4-\vec e_3$$ and $$\epsilon :\vec e_1 \vec e_2\vec e_3\vec e_4=5$$. How I can define the tensor T so I can find its determinant and eigenvalues?