Numpy matrix(array) rationale

Question

I am so confused about Numpy array. Let's say I have two Numpy arrays.

a = np.array([[1,2], [3,4], [5,6]])
b = np.array([[1,10], [1, 10]])

My interpretations of a and b are 3x2 and 2x2 matrices, i.e,

a = 1 2    b = 1 10
    3 4        1 10
    5 6

Then, I thought it should be fine to do a * b since it is a multiplication of 3x2 and 2x2 matrices. However, it was not possible and I had to use a.dot(b).

Given this fact, I think my intepretation of Numpy array is not right. Can anyone let me know how I should think of Numpy array? I know that I can do a*b if I convert a and b into np.matrix. However, looking at other's code, it seems that people are just fine to use Numpy array as matrix, so I wonder how I should understand Numpy array in terms of matrix.

If you are on Python 3.5, you can use a @ b to do what you want. a * b does an elementwise multiplication. — SethMMorton
– SethMMorton, Commented Nov 8, 2016 at 4:27
Also, to check if you're dimensions match, you can try .shape to see the dimensions. Then, if you find out that the dimensions don't match, you can transpose it. :) — user2639830
– user2639830, Commented Nov 8, 2016 at 4:30
Both kinds of multiplicatin are useful. Look at MATLAB code, you'll see both a*b and a.*b. — hpaulj
– hpaulj, Commented Nov 8, 2016 at 4:30

Mark Hannel · Accepted Answer · 2016-11-08 15:24:43Z

2

For numpy arrays, the * operator is used for element by element multiplication of arrays. This is only well defined if both arrays have the same dimensions. To illuminate *-multiplication, note that element by element multiplication with the identity matrix will not return the same matrix

>>> I = np.array([[1,0],[0,1]])
>>> B = np.array([[1,2],[3,4]])
>>> I*B
array([[ 1, 0], 
       [ 0, 4]])

Using the numpy function dot(a,b) produces the typical matrix multiplication.

>>> dot(I,B)
array([[ 1, 2],
       [ 3, 4]])

edited Nov 8, 2016 at 15:24

answered Nov 8, 2016 at 5:06

Mark Hannel

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2 Comments

P. Camilleri Over a year ago

How is there a 10 on your result (I*B) 2nd column, 2nd line?

Mark Hannel Over a year ago

Thanks for the catch! I accidentally copied and pasted the wrong multiplication from my terminal. Error corrected above.

travelingbones · Accepted Answer · 2016-11-08 05:05:31Z

1

np.dot is probably what you're looking for?

a = np.array([[1,2], [3,4], [5,6]])

b = np.array([[1,10], [1, 10]])

np.dot(a,b)

Out[6]:
array([[  3,  30],
       [  7,  70],
       [ 11, 110]])

answered Nov 8, 2016 at 5:05

travelingbones

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