I would like to compute the double dot product between a 2nd and 4th rank tensor in mathematica $A_{kl}A_{ijkl}$
$if \, A_{kl}=\begin{pmatrix} 1& 0 & 0\\ 0 & 1 & 0\\ 0&0 & 1 \end{pmatrix} \, and \, \, A_{ijkl}=\begin{pmatrix} 1 &0 &0 &0 &1 &0& 0& 0& 1\\ 0 &0 &0 &0 &0 &0 &0 &0 &0\\ 0 &0 &0 &0 &0 &0 &0 &0& 0&\\ 0& 0& 0& 0& 0& 0& 0& 0& 0&\\ 1& 0& 0& 0& 1& 0& 0& 0& 1&\\ 0& 0& 0& 0& 0& 0& 0& 0& 0&\\ 0& 0& 0& 0& 0& 0& 0& 0& 0&\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 1& 0& 0& 0& 1 \end{pmatrix} then \, A_{kl}A_{ijkl} = \begin{pmatrix} 3&0 &0 \\ 0 &3 &0 \\ 0 &0 &3 \end{pmatrix}$
Can anyone give me a hand with this?
Best Regards