🔒 HOW does 3D NumPy array actually do matrix multiplication

[little bramble]

I'm trying to understand, how does 3D NumPy arrat actually do matrix multiplication under with hood (np.matmul (arr1, arr2))

import numpy as np
arr1 = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])
arr2 = np.array([[[4, 5, 6], [3, 2, 1]], [[7, 8, 9], [12, 10, 11]]])
print(np.matmul(arr1, arr2))
#this throws an error, 
#by going through the error, i find out that, arr1's shape(x,p,n) and arr2's shape #should be(x,n,p)
#that is last dimension of arr1=2nd last dimension of arr2
#but why is that, and what's the actual mathematical operation..

#help me to understand

[lucid edge]

@little bramble

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[cosmic wagon]

My general understanding has always been that the two arrays should be the same shape.

[shell rapids]

You've read this?
https://numpy.org/doc/stable/reference/generated/numpy.matmul.html#numpy-matmul
(I expect you have. But that's where I'd start.)

[cosmic wagon]

Which apparently is incorrect.

[shell rapids]

@little bramble ^^

[cosmic wagon]

The shapes have to be compatible.

But numpy being numpy, the shapes don't necessarily have to be equal.

[little bramble]

shape dosen't need to equal, but for 3D array multi, mxn should only multiplie with nxp not pxn like the traditional mathematics

[little bramble]

i think that always dosen't need to.

[little bramble]

yes, and i think i have the ans.

3D array multiplication follows the 'batch multiplication matrix rule'
and after going through some example, now it's clear

[lucid edge]

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