The NumPy library is very helpful for solving linear systems in python. For instructions on how to install NumPy look here.
Matrixes in Python
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 is
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| language | py |
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| title | Creating a matrix |
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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 :
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| language | py |
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| title | Indexing matrix |
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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.
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np.linalg.solve(a,b) #where a and b is matrixs
#returns a array with solutions to the system |
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| language | py |
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| title | Eigenvalues and eigenvectors |
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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 |
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| language | py |
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| title | Determinant |
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np.linalg.det(a) # where a is a square matrix
#returns the determinant of the matrix a |
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| language | py |
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| title | Finding the inverse |
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np.linalg.inv(a) # where a is the matrix to be inverted
#Returns the inverse matrix of a |
Example
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| language | py |
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| title | Solving set of equations |
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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 |
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