Vectors¶

Create Vectors¶

Lets create a vector containing shopped fruit:

import numpy as np
from matplotlib import pyplot as plt

# apples, bananas, cherries
a = np.array([3, 1, 50])

Create a second vector that lists another shopping session for the same types of fruit in the same order

b = ...

Add both fruit vectors together:

fruit = a + b
fruit

Now shop 10 times as much

fruit = fruit * ...

Plot the vector:

plt.bar(fruit)
# plt.show()  # if not running in Jupyter

Define a set of fruit prices

prices = np.array([1.0, 0.5, 0.05])

See how much each position costs

fruit * prices

The dot product calculates the total amount on the bill:

np.dot(fruit, prices)

The cross product does not make much sense with fruit shopping. Instead, define two x, y, z vectors:

a = np.array([2, 0, 0])
b = np.array([0, 1, 0])
np.cross(a, b)

Check the following:

what happens if you swap the arguments of the cross product?
what happens if you calculate the cross products of a vector with itself?
what happens if you calculate a dot product from a with the cross product of a and b?

Which vectors are colinear, which are orthogonal?

a = np.array([1, 2])
b = np.array([-1, -2])
c = np.array([2, 4])
d = np.array([1, -2])
e = np.array([-2, 1])

Create a large vector

a = np.arange(100)

Create a vector with interpolated numbers

b = np.linspace(10, 20, 100)

Draw a parabola by filling the gaps:

x = np.linspace(...)
y = ...
plt.plot(x, y)

Plot a random vector:

v = np.random.normal(0, 10, 1000)
plt.plot(v)