Vector Arithmetic

Vector arithmetic applies addition and/or subtraction operations at respective corresponding positions across vectors in an equation. For example, applying arithmetic on three vectors can look like the following:

$$ \begin{bmatrix} a \\ b \\ c \end{bmatrix} + \begin{bmatrix} d \\ e \\ f \end{bmatrix} - \begin{bmatrix} g \\ h \\ i \end{bmatrix} = \begin{bmatrix} a + d - g \\ b + e - h \\ c + f - i \end{bmatrix}$$

Implementation in Python Numpy

$$ \begin{bmatrix} 2 \\ 3 \\ 1 \end{bmatrix} + \begin{bmatrix} 8 \\ 4 \\ 5 \end{bmatrix} - \begin{bmatrix} 3 \\ 5 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 + 8 - 3 \\ 3 + 4 - 5 \\ 1 + 5 - 1 \end{bmatrix} = \begin{bmatrix} 7 \\ 2 \\ 5 \end{bmatrix}$$

import numpy as np

# defining the vectors
vect_1 = np.array([2,3,1])
vect_2 = np.array([8,4,5])
vect_3 = np.array([3,5,1])

# implementing the operation above
vect_1 + vect_2 - vect_3

array([7, 2, 5])