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I would like the following sum for the matrices $A,B$, both $n \times n$:

\begin{align} \sum(A_{ij} \cdot B_{jk} \cdot A_{kz} \cdot B_{zf}) & \text{ for all } j,k,z,f \text{ such that } i≠k,j≠z,k≠f \end{align}

Is there a way to get at this sum using matrix multiplication? Any ideas?

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adam levin
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  • If you multiply A by B and then set the diagonal elements to 0 you get sum(Aij•Bjk) over all j,k such that i≠k. So sum(Akz•Bzf) over all z,f such that k≠f can be got from the same procedure. However if you take this resulting matrix and square it then sum over each row, the result is not the same as the sum I desire. – adam levin Apr 12 '14 at 01:13
  • Update: Progress been made... http://mymathforum.com/linear-algebra/42813-can-i-calculate-sum-using-matrix-multiplication.html – adam levin Apr 12 '14 at 16:41

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