# Re: [sympy] tensor products and/or multidimensional matrix multiplication

```Hopefully something in the tensor module could help you here (I'll
defer that to someone more knowledgeable). Otherwise you'd need
something like MatrixFunction (which isn't implemented yet,
https://github.com/sympy/sympy/issues/5855), i.e., to represent the
matrices as functions of i and j.```
```
Aaron Meurer

On Mon, Oct 17, 2016 at 7:43 PM, Andre Walker-Loud <walksl...@gmail.com> wrote:
> Greetings,
>
> I am using sympy for the first time, and attempting to do matrix
> multiplication like the following
>
> sum_{l,m} U[i,l] G[l,m] D[j,m]
>
> I want to do regular matrix multiplication, but only on one of the two
> indices for the objects U and D, in my case for a known G (I want to put
> numerical entries for the matrix G).  I was hoping to have this print out a
> symbolic expression.  I found sympy.MatrixSymbol to create a symbolic
> representation for U and D, but it seems I need some functionality from
> sympy.tensor class to handle this type of multiplication.
>
> Does anyone have, or could anyone write down a simple example doing such a
> multiplication?  Let me make a simple specific example.
> Let
>
> G = sympy.Matrix([[0,1], [-1,0]]) #
> # [ 0  1 ]
> # [ -1 0 ]
>
> So, in the above example, leaving i,j arbitrary, this would result in
>
> U[i,0] D[j,1] - U[i,1] D[j,0]
>
> I also want to multiply this by a G[i,j], but knowing how to do the above I
> think will be sufficient for the complete multiplication.
>
> Thanks,
> Andre
>
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