Matrixes in Python
Like many other programming languages, the indices in Python arrays starts at 0. This is commonly known, but may catch you by surprise if you're used to the indices in e.g. Matlab.
In Python, matrices are not it's own thing, but rather a list of list/nested lists. Let's look at an example:
Our matrix of choice will be To represent this matrix in python, we will consider the matrix as two independent lists,
and
, put together in one list. Written in code, it looks like this:
mat1 = [[1, 2, 3], [4, 5, 6]] # To make the matrices easier to read while coding, we can place the different lists vertical to eachother instead of horizontally. mat2 = [[1, 2, 3], [4, 5, 6]] # Printing both of these matrices will result in the same output: [[1, 2, 3], [4, 5, 6]] # To alter the output to a more readable format, for-loops are very helpful: [[1, 2, 3], [4, 5, 6]]
Now, let's see how to obtain different values from our matrix:
A = [[1, 2, 3],
[4, 5, 6]]
print("A =", A)
print("A[1] =", A[1]) # 2nd row
print("A[1][2] =", A[1][2]) # 3rd element of 2nd row
print("A[0][-1] =", A[0][-1]) # Last element of 1st Row
column = []; # Empty list
for row in A:
column.append(row[2]) # Adding the element in the third column of every row-list.
print("3rd column =", column)
The script above will result in the following output:
A = [[1, 2, 3], [4, 5, 6]] A[1] = [4, 5, 6] A[1][2] = 6 A[0][-1] = 3 3rd column = [3, 6]
Matrixes in Python using NumPy
a = np.array([[1,2],[3,4]])
In Python rows and columns start at 0. For example index the data at first row second column :
b = a[0,1]
Linear algebra using NumPy
NumPy has several useful functions for linear algebra built-in. For full list look check the NumPy documentation.
np.linalg.solve(a,b) #where a and b is matrixs #returns a array with solutions to the system
np.linalg.eig(a) # where a is a square matrix #returns two arrays [v,w] #v containing the eigenvalues of a #w containing the eigenvectors of a
np.linalg.det(a) # where a is a square matrix #returns the determinant of the matrix a
np.linalg.inv(a) # where a is the matrix to be inverted #Returns the inverse matrix of a
Example
import numpy as np # Solving following system of linear equation # 5a + 2b = 35 # 1a + 4b = 49 a = np.array([[5, 2],[1,4]]) # Lefthand-side of the equation b = np.array([35, 94]) #Righthand-side print(np.linalg.solve(a,b)) #Printing the solution