MathABC: Simple Vector

Ordered list of numbers is the algebraic interpretation of a vector; the geometric interpretation of a vector is a straight line with a specific length (also called magnitude) and direction (also called angle; it is computed relative to the positive x-axis).

References 

Cohen, Mike X. Practical Linear Algebra for Data Science (p. 24). O'Reilly Media. Kindle Edition. 

Code From the Book

# import libraries

import numpy as np

import matplotlib.pyplot as plt

# NOTE: these lines define global figure properties used for publication.

import matplotlib_inline.backend_inline

matplotlib_inline.backend_inline.set_matplotlib_formats('svg') # display figures in vector format

plt.rcParams.update({'font.size':14}) # set global font size

# create a vector

v = np.array([-1,2])

# plot that vector (and a dot for the tail)

plt.arrow(0,0,v[0],v[1],head_width=.1,width=.01)

plt.plot(0,0,'ko',markerfacecolor='k',markersize=7)

# add axis lines

plt.plot([-3,3],[0,0],'--',color=[.8,.8,.8],zorder=-1)

plt.plot([0,0],[-3,3],'--',color=[.8,.8,.8],zorder=-1)

# make the plot look nicer

plt.axis('square')

plt.axis([-3,3,-3,3])

plt.xlabel('')

plt.ylabel('')

plt.title('Vector v in standard position')

plt.show()