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How to Create a Matrix in Python: Guide

How to Create a Matrix in Python: Guide
Hostman Team
Technical writer
Python
11.12.2023
Reading time: 9 min

Matrices are one of the basic objects in mathematics. They allow you to represent and manipulate data as a table consisting of rows and columns. They are used to solve systems of linear equations, define matrix actions, transform coordinates, and much more.

In this article, we will describe several ways to create a matrix in Python. Additionally, we will look at some basic operations such as addition, multiplication, and defining an inverse matrix.

What is a matrix?

A matrix is a table of numbers used in math and engineering to represent data. Matrices take the form of a table consisting of rows and columns. Each element has a unique index that denotes the row and column in which it is located. For example, a 3x3 matrix will have 3 rows and 3 columns, and each element will have an index like (i, j), where i is the row number and j is the column number.

Creating a matrix

There are several ways to create a matrix in Python. There are some of them:

  • With lists. You can create a matrix using nested lists. Each nested list will correspond to one row. This is how you can create a square Python matrix:

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
  • With NumPy. NumPy is a library for mathematical calculations and data processing. It has an Array class that can be used to create a matrix:

import numpy as np 
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

If you need to perform standard mathematical operations with matrices, you should choose NumPy. It is easier to use, and all operations are already implemented in the library. But if you want to create your own methods, for example, for educational purposes, or if you plan to perform non-standard manipulations, use nested lists. 

Now, let's look at matrix operations and work with them using nested lists and NumPy.

Matrix Operations

Here is a list of basic manipulations:

  • Addition. You can add two matrices if their dimensions are the same. Each element of the resulting matrix will equal the sum of the corresponding elements of the original matrices.

  • Subtraction. One matrix can be subtracted from another if their dimensions are the same. Each element of the resulting matrix will equal the difference of the corresponding elements of the original matrices.

  • Multiplication by a number. Each element of the final matrix will be equal to the product of the corresponding element of the original matrix by a number.

  • Multiplication of two matrices. Matrices can be multiplied if the number of columns of the first matrix equals the number of rows of the second matrix. The result will be a new matrix with the size corresponding to the number of rows of the first matrix and the number of columns of the second matrix. We will describe this operation in more detail later.

  • Matrix transpose. Transpose is an operation in which rows and columns are swapped. That is, the first column becomes the first row, the second column becomes the second row, and so on.

  • Inverse of a matrix. Matrix B will be the inverse matrix for matrix A if the result of the operation A*B is an identity matrix.

-

Addition

It is important to remember that when adding two matrices, their sizes must match.

Here is an example of addition using nested lists and loops:

matrix1 = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 
matrix2 = [[9, 8, 7], [6, 5, 4], [3, 2, 1]] 
result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

for i in range(len(matrix1)): 
         for j in range(len(matrix1[0])): 
                  result[i][j] = matrix1[i][j] + matrix2[i][j] 

print(result)

The result:

[[10, 10, 10], [10, 10, 10], [10, 10, 10]]

Here's a similar addition using the add() method from the NumPy library:

import numpy as np 

matrix1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) 
matrix2 = np.array([[9, 8, 7], [6, 5, 4], [3, 2, 1]]) 
result = np.add(matrix1, matrix2)

print(result)

The result:

[[10 10 10]
[10 10 10]
[10 10 10]]

Subtraction 

In Python, you can perform matrix subtraction using a loop or the subtract() method from the NumPy library. When subtracting, the dimensions must match.

Subtracting with a loop:

matrix1 = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 
matrix2 = [[9, 8, 7], [6, 5, 4], [3, 2, 1]] 
result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] 

for i in range(len(matrix1)): 
         for j in range(len(matrix1[0])): 
                  result[i][j] = matrix1[i][j] - matrix2[i][j] 

print(result)

The result:

[[-8, -6, -4], [-2, 0, 2], [4, 6, 8]]

Subtraction using the subtract() method from the NumPy library:

import numpy as np 

matrix1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) 
matrix2 = np.array([[9, 8, 7], [6, 5, 4], [3, 2, 1]]) 

result = np.subtract(matrix1, matrix2)

print(result)

The result:

[[-8 -6 -4]
[-2 0 2]
[ 4 6 8]]

Multiplication by a number

In Python, multiplying a matrix by a number can be implemented using a loop or the dot() method from the NumPy library.

When multiplying a matrix by a number, each element is multiplied by that number.

Multiplication using a loop:

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 
scalar = 2 
result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] 

for i in range(len(matrix)): 
        for j in range(len(matrix[0])): 
                 result[i][j] = matrix[i][j] * scalar

print(result)

The result:

[[2, 4, 6], [8, 10, 12], [14, 16, 18]]

Here is an example of how the dot() method from the NumPy library works with the same data:

import numpy as np 

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
scalar = 2 

result = np.dot(matrix, scalar)

print(result)

The result:

[[ 2 4 6]
[ 8 10 12]
[14 16 18]]

You can also use the multiplication operation sign * instead of the dot() method:

import numpy as np 

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) 
scalar = 2 

result = matrix * scalar 

print(result)

The result:

[[ 2 4 6]
[ 8 10 12]
[14 16 18]]

In most cases, the dot() method is faster than manually implemented loops.

Multiplication of two matrices

This operation results in a new matrix with the number of rows of the first matrix and the number of columns of the second matrix. In matrix multiplication, the number of columns of the first matrix must match the number of rows of the second matrix. Each element of the new matrix is the sum of the product of the row elements of the first matrix and the column elements of the second matrix, as in the picture below:

Image1

As before, we implement the product using loops and NumPy.

Multiplication implemented on loops can look like this:

matrix1 = [[1, 2], [3, 4]] 
matrix2 = [[5, 6], [7, 8]] 
result = [[0, 0], [0, 0]] 

for i in range(len(matrix1)): 
        for j in range(len(matrix2[0])): 
                 for k in range(len(matrix2)): result[i][j] += matrix1[i][k] * matrix2[k][j]


print(result)

The result: 

[[19, 22], [43, 50]]

NumPy uses the dot() method for matrix multiplication:

import numpy as np 

matrix1 = np.array([[1, 2], [3, 4]]) 
matrix2 = np.array([[5, 6], [7, 8]]) 

result = np.dot(matrix1, matrix2)

print(result)

The result:

[[19 22]
[43 50]]

The @ operation works similarly to the dot() method:

import numpy as np 

matrix1 = np.array([[1, 2], [3, 4]]) 
matrix2 = np.array([[5, 6], [7, 8]])

result = matrix1 @ matrix2

print(result)

The result:

[[19 22]
[43 50]]

Using the dot() method or the @ operator gives faster results than using manually implemented loops. 

Remember that the multiplication is a non-commutative operation, i.e., the order of matrix multiplication matters, and the result will be different if you rearrange them.

Matrix transpose

Transpose is an operation that turns the rows of the original matrix into the columns of the new matrix, and the columns into the rows.

In Python, you can perform a transpose using the T property or the transpose() method from the NumPy library.

An example of transpose using the T property:

import numpy as np 

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

result = matrix.T

print(result)

The result:

[[1 4 7]
[2 5 8]
[3 6 9]]

And an example of transpose using the transpose() method:

import numpy as np

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

result = np.transpose(matrix)

print(result)

The result:

[[1 4 7]
[2 5 8]
[3 6 9]]

In both cases, the result is the same.

Using a loop, the transposition can be realized as follows:

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 
result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

for i in range(len(matrix)):
        for j in range(len(matrix[0])):
                 result[j][i] = matrix[i][j] 

print(result)

The result:

[[1, 4, 7], [2, 5, 8], [3, 6, 9]]

This method can be slow and inefficient for large matrices, so NumPy is recommended for a faster and more efficient solution.

Finding the inverse of a matrix

An inverse matrix is a matrix that, when multiplied by the original matrix, results in an identity matrix (with ones on the diagonal and zeros in the remaining cells).

In Python, you can find an inverse matrix using the inv() method from the NumPy library.

import numpy as np 

matrix = np.array([[1, 2], [3, 4]]) 

result = np.linalg.inv(matrix)

print(result)

The result:

[[-2. 1. ]
[ 1.5 -0.5]]

If the matrix does not have an inverse matrix, the inv() method will raise the LinAlgError: Singular matrix exception.

To check if a matrix has an inverse, use the det() method from the NumPy library, which returns the determinant of the matrix. If the determinant is zero, the matrix is singular, and it has no inverse matrix:

import numpy as np

matrix = np.array([[1, 2], [3, 4]])
determinant = np.linalg.det(matrix)

if determinant == 0:
         print("The matrix does not have an inverse.")
else:
         result = np.linalg.inv(matrix)
       print(result)

Finding the inverse matrix using loops can be quite complicated and time-consuming, especially for large matrices. Therefore, we recommend using NumPy.

Managed solution for Backend development

Conclusion

Matrices are an important concept in linear algebra and are often used in various fields, such as artificial intelligence, graphics, and optimization. Python provides many tools for working with matrices, including the NumPy library. Understanding matrices and their operations can help solve many practical problems in various fields.

If you want to build a web service using Python, you can rent a cloud server at competitive prices with Hostman.

Python
11.12.2023
Reading time: 9 min

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Configuring the Gunicorn Service and Socket First, create the service configuration file: sudo nano /etc/systemd/system/gunicorn.service Add the following content to the file: [Unit] Description=gunicorn daemon Requires=gunicorn.socket After=network.target [Service] Type=notify User=someuser Group=someuser RuntimeDirectory=gunicorn WorkingDirectory=/home/someuser/myapp ExecStart=/path/to/venv/bin/gunicorn wsgi:app ExecReload=/bin/kill -s HUP $MAINPID KillMode=mixed TimeoutStopSec=5 PrivateTmp=true [Install] WantedBy=multi-user.target Make sure to replace /path/to/venv/bin/gunicorn with the actual path to the Gunicorn executable within your virtual environment. It will likely look something like this: /home/someuser/myapp/venv/bin/gunicorn. Next, create the socket configuration file: sudo nano /etc/systemd/system/gunicorn.socket Add the following content: [Unit] Description=gunicorn socket [Socket] ListenStream=/run/gunicorn.sock SocketUser=www-data [Install] WantedBy=sockets.target Enable and start the socket with: systemctl enable --now gunicorn.socket Configuring Gunicorn Let's review some useful parameters for Gunicorn in Python 3. You can find all possible parameters in the official documentation. Sockets -b BIND, --bind=BIND — Specifies the server socket. You can use formats like: $(HOST), $(HOST):$(PORT). Example: gunicorn --bind=127.0.0.1:8080 wsgi:app This command will run your application locally on port 8080. Worker Processes -w WORKERS, --workers=WORKERS — Sets the number of worker processes. Typically, this number should be between 2 to 4 per server core. Example: gunicorn --workers=2 wsgi:app Process Type -k WORKERCLASS, --worker-class=WORKERCLASS — Specifies the type of worker process to run. By default, Gunicorn uses the sync worker type, which is a simple synchronous worker that handles one request at a time. Other worker types may require additional dependencies. Asynchronous worker processes are available using Greenlets (via Eventlet or Gevent). Greenlets are a cooperative multitasking implementation for Python. The corresponding parameters are eventlet and gevent. We will use an asynchronous worker type compatible with aiohttp: gunicorn wsgi:app --bind localhost:8080 --worker-class aiohttp.GunicornWebWorker Access Logging You can enable access logging using the --access-logfile flag. Example: gunicorn wsgi:app --access-logfile access.log Error Logging To specify an error log file, use the following command: gunicorn wsgi:app --error-logfile error.log You can also set the verbosity level of the error log output using the --log-level flag. Available log levels in Gunicorn are: debug info warning error critical By default, the info level is set, which omits debug-level information. Installing and Configuring Nginx First, install Nginx with the command: sudo apt install nginx Let’s check if the Nginx service can connect to the socket created earlier: sudo -u www-data curl --unix-socket /run/gunicorn.sock http If successful, Gunicorn will automatically start, and you'll see the HTML code from the server in the terminal. Nginx configuration involves adding config files for virtual hosts. Each proxy configuration should be stored in the /etc/nginx/sites-available directory. To enable each proxy server, create a symbolic link to it in /etc/nginx/sites-enabled. When Nginx starts, it automatically loads all proxy servers in this directory. Create a new configuration file: sudo nano /etc/nginx/sites-available/myconfig.conf Then create a symbolic link with the command: sudo ln -s /etc/nginx/sites-available/myconfig.conf /etc/nginx/sites-enabled Nginx must be restarted after any changes to the configuration file to apply the new settings. First, check the syntax of the configuration file: nginx -t Then reload Nginx: nginx -s reload Conclusion Gunicorn is a robust and versatile WSGI server for deploying Python applications, offering flexibility with various worker types and integration options like Nginx for load balancing and reverse proxying. Its ease of installation and configuration, combined with detailed logging and scaling options, make it an excellent choice for production environments. By utilizing Gunicorn with frameworks like aiohttp and integrating it with Nginx, you can efficiently serve Python applications with improved performance and resource management.
23 October 2024 · 7 min to read

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