Numpy Matrix Subtraction Confusion

Question

I have a question about the result of an operation I accidentally performed with two numpy matrices (and later fixed).

Let\'s say that I have a column vector, A = [1,2,

Answer 1

I cannot really explain the rationale, because I often use np.matrix instead of np.array to prevent this sort of thing. Thanks to @Jaime's link in the comments above, it's clear that np.matrix is simply a subclass from np.ndarray with redefined infix operations where there is an appropriate answer from linear algebra. Where there isn't, it falls back on the rules from np.ndarray with ndim = 2.

It seems that addition follows the matrix multiplication rules for which elements from A are paired with which elements from B:

In [1]: import numpy as np
In [2]: A = np.matrix([1,2,3]).T
In [3]: B = np.matrix([1,1,1])

In [4]: A
Out[4]: 
matrix([[1],
        [2],
        [3]])

In [5]: B
Out[5]: matrix([[1, 1, 1]])

In [6]: A+B
Out[6]: 
matrix([[2, 2, 2],
        [3, 3, 3],
        [4, 4, 4]])

In [7]: A*B
Out[7]: 
matrix([[1, 1, 1],
        [2, 2, 2],
        [3, 3, 3]])

This is the same behavior you get with np.array:

In [9]: a = np.arange(3)[...,None]

In [10]: b = np.arange(3)

In [11]: a
Out[11]: 
array([[0],
       [1],
       [2]])

In [12]: b
Out[12]: array([0, 1, 2])

In [13]: a+b
Out[13]: 
array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4]])