# [Numpy-discussion] vectorized multi-matrix multiplication

Jonathan Taylor jtaylor@cs.toronto....
Sun Aug 26 11:49:29 CDT 2012

```Assuming matrices1 and matrices2 are actually arrays of size (N, 3, 3)
you can do:

np.einsum('nij,njk->nik', matrices1, matrices2)

On Sun, Aug 26, 2012 at 11:04 AM, Alex Flint <alex.flint@gmail.com> wrote:
> I have two lists of 3x3 arrays and I would like to compute the matrix
> product of the i-th element in the first list with the i-th element in
> the second list. Of course, I could just loop over the lists:
>
> for i in range(n):
>      out[i] = dot( matrices1[i], matrices2[i] )
>
> However, the list is quite long, and each matrix is very small (3x3)
> so this turns out to be quite slow. Is there a way to do this with a
> single numpy call? I have looked at tensordot but it outputs an N x N
> x 3 x 3 array, whereas I want an N x 3 x 3 output. I've also looked at
> various broadcasting tricks but I haven't found anything that works
> yet.
>
> Alex
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```