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 = [1,2,3], and a row vector B = [1,1,1]. As far as I know there is no correct mathematical way to "subtract" these two vectors, i.e. this should be an undefined operation. And yet, when I do so, I get back:

>>> matrix([[0, 1, 2],
            [0, 1, 2],
            [0, 1, 2]])

I thought that this might be some sort of broadcasting operation, but this still troubles me a bit. Shouldn't numpy.matrix objects only contain mathematically valid matrix operations?

Any help is appreciated!

Thanks!

Answer 1

A and B are being broadcasted together:

A = np.matrix([[1],[2],[3]])
#a 3x1 vector
#1
#2
#3

B = np.matrix([[1,1,1]])
#a 1x3 vector
#1 1 1

A-B
#a 3x3 vector
#0 0 0
#1 1 1
#2 2 2

A gets broadcasted along its size 1 dimension(columns) into

#1 1 1
#2 2 2
#3 3 3

B get broadcasted along its size 1 dimension(rows) into

#1 1 1
#1 1 1
#1 1 1

Then A-B is computed as usual for two 3x3 matrices.

If you want to know why it does this instead of reporting an error it's because np.matrix inherits from np.array. np.matrix overrides multiplication, but not addition and subtraction, so it uses the operations based on the np.array, which broadcasts when the dimensions allow it.