Dot Product

Dot product (also known as scalar product) is an operation from linear algebra that takes two equally sized vectors (vector is a sequence of numbers) and returns a single number

How it works

 Example 1

vector1 = [1, 2, 3]

vector2 = [4, 5, 6]

dot product of vector1 and vector2:

1 * 4 + 2 * 5 + 3 * 6 = 32

Example 2

When multiplying vectors, one must be vertical (shape: (X, 1)) and the other must be horizontal (shape: (1, X))

Vector1 = 

Vector2 = 

The dot product is the sum of multiplying each corresponding index number of each vector.

Dot Product:

Dot product with Numpy

The syntax in Numpy is np.dot() 

Example 3

Dot product of two 1D Numpy arrays

ary1 = np.array([1, 4, 2])
ary2 = np.array([2, 5, 7])
np.dot(ary1, ary2) # 1*2 + 4*5 + 2*7
>>> 36

Example 4

Dot product of 1D Numpy array and scalar (a number)

ary1 = np.array([1, 4, 2])
num1 = 5
np.dot(ary1, num)
>>> [ 5, 20, 10]

It behaves as if we multiplied the array with scalar: ary1 * 5

If one of the arrays is a 2D array, the np.dot will perform a matrix multiplication which is covered in the next lesson.