2列向量的Numpy内积

Question

How can I take an inner product of 2 column vectors in python's numpy

Below code does not work

import numpy as np
x = np.array([[1], [2]])
np.inner(x, x)

It returned

array([[1, 2],
       [2, 4]])`

instead of 5

Answer 1

The inner product of a vector with dimensions 2x1 (2 rows, 1 column) with another vector of dimension 2x1 (2 rows, 1 column) is a matrix with dimensions 2x2 (2 rows, 2 columns). When you take the inner product of any tensor the inner most dimensions must match (which is 1 in this case) and the result is a tensor with the dimensions matching the outter, ie; a 2x1 * 1x2 = 2x2.

What you want to do is transpose both such that when you multiply the dimensions are 1x2 * 2x1 = 1x1.

More generally, multiplying anything with dimensions NxM by something with dimensions MxK , yields something with dimensions NxK . Note the inner dimensions must both be M . For more,review your matrix multiplication rules

The np.inner function will automatically transpose the second argument, thus when you pass in two 2x1, you get a 2x2, but if you pass in two 1x2 you will get a 1x1.

Try this:

import numpy as np
x = np.array([[1], [2]])
np.inner(np.transpose(x), np.transpose(x))

or simply define your x as row vectors initially.

import numpy as np
x = np.array([1,2])
np.inner(x, x)

Answer 2

i think you mean to have:

x= np.array([1,2])

in order to get 5 as output, your vector needs to be 1xN not Nx1 if you want to apply np.inner on it

Answer 3

尝试以下它会起作用

np.dot(np.transpose(a),a))

Answer 4

make sure col_vector has shape (N,1) where N is the number of elements

then simply sum one to one multiplication result

np.sum(col_vector*col_vector)