I am trying to decuct the formula:
$\text{adj}(\mathbf{T})_{ij} = 0.5 \epsilon_{ipq} \epsilon_{jrs} T_{pr} T_{qs}$
from the definition:
$\text{adj}(\mathbf{T})(\mathbf{u} \times \mathbf{v}) = (\mathbf{T} \mathbf{u}) \times (\mathbf{T} \mathbf{v})$
where $\mathbf{T}$ is an arbitray second order Tensor and $\mathbf{u},\mathbf{v}$ are arbitray vectors, $\times$ is the cross product and the dot product between a second order Tensor and a vector is denoted by $\mathbf{T} \mathbf{v}$.
I am stuck at this point:
$\text{adj}(\mathbf{T})_{om} u_i v_j \epsilon_{ijm} = T_{ij} T_{kl} \epsilon_{iko} u_j v_l$
and I don't know how to get rid of u and v to get the required formula?
Thanks for your Help.