Numpy - Dot Product of a Vector of Matrices with a Vector of Scalars

If your NumPy is new enough (1.6 or better), you could use numpy.einsum:

result = np.einsum('ijk,i -> jk', data, vector)

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In [36]: data = np.array ([[[1,1,1,1],[2,2,2,2],[3,3,3,3]], [[3,3,3,3],[4,4,4,4],[5,5,5,5]]])

In [37]: vector = np.array ([10,20])

In [38]: np.einsum('ijk,i -> jk', data, vector)
Out[38]: 
array([[ 70,  70,  70,  70],
       [100, 100, 100, 100],
       [130, 130, 130, 130]])

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Or, without np.einsum, you could add extra axes to vector and take advantage of broadcasting to perform the multiplication:

In [64]: (data * vector[:,None,None]).sum(axis=0)
Out[64]: 
array([[ 70,  70,  70,  70],
       [100, 100, 100, 100],
       [130, 130, 130, 130]])