Matrices¶

In this exercise, you continue using vectors to calculate the price of fruit baskets. This time, you will need matrices.

Define a matrix containing a shopping list for two people. Each row is a person, the columns are the fruit types (apple, banana, cherry).

import numpy as np
from matplotlib import pyplot as plt

M = np.array([10, 2, 0],
             [4, 7, 10])

Inspect the shape¶

Inspect the shape, your most important debugging operation:

M.shape

Hint

Put this command under your pillow, really. When working with vectors and matrices in Python, you will need to inspect the shape before googling or doing anything else. While I was learning this line of work, 50% of my bugs had to do with wrong shapes.

Matrix arithmetics¶

Not too exciting, but you might want to try them out anyway:

M + 10

M * 5

Transposition¶

Swap the axes - note that this is not a rotation.

M.transpose()
M.transpose().shape

Multiplying matrices with vectors¶

Which of the following dot products work? Try them one by one and check the shapes to explain your observation

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

np.dot(M, prices)
np.dot(prices, M)
np.dot(M.transpose(), prices)
np.dot(prices, M.transpose())

Create a matrix from two vectors¶

Create a matrix from a row and column vector and plot it:

a = np.arange(100)
b = a.reshape(100, 1)
c = a.reshape(1, 100)
d = b * c
print(d.shape)
plt.imshow(d)

Useful phrases¶

B = np.arange(6).reshape((2, 3))

Position-wise multiplication, if matrices have the same size:

M * B

Create a random matrix:

M = np.random.randint(low=0, high=5, size=(3, 4))

Plot a matrix:

plt.imshow(M)