Vector Outer Product

Introduction

• The Vector Outer Product is a method of multiplying two vectors and receiving a matrix as the result.
• The first vector must be a column vector, while the second must be a row vector.
• The two vectors do not need to be the same size.
• The order of the resulting matrix will have the same number of rows as the first vector, and the same number of columns as the second vector.
• Each element in the resulting matrix will be the product of corresponding elements from the two vectors.

Example

1. First we position them to make it easier to see which elements need to be multiplied:
2. And solve: Note that we write the product as ab' as b needs to be a row vector.

code (Python)

import numpy as np

a = [6, 5]
b = [4, 3, 8]

c = np.outer(a, b)
print(c)