Python Program to Perform Matrix Multiplication

Posted in Python Tutorial

Updated on Oct 31, 2024

By Mari Selvan

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4 mins

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Python Program to Perform Matrix Multiplication

Photo Credit to CodeToFun

Introduction

Matrix multiplication is a fundamental operation in linear algebra and computer science. It involves multiplying two matrices to produce a third matrix.

In this tutorial, we will explore a python program that performs matrix multiplication.

We'll break down the logic step by step and provide a sample implementation.

Example

Let's dive into the python code that performs matrix multiplication.

multiply_matrices.py

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# Function to perform matrix multiplication
def multiply_matrices(first_matrix, second_matrix):
    result_matrix = [[0 for _ in range(len(second_matrix[0]))] for _ in range(len(first_matrix))]

    # Perform matrix multiplication
    for i in range(len(first_matrix)):
        for j in range(len(second_matrix[0])):
            for k in range(len(second_matrix)):
                result_matrix[i][j] += first_matrix[i][k] * second_matrix[k][j]

    return result_matrix

# Function to display a matrix
def display_matrix(matrix):
    for row in matrix:
        print('\t'.join(map(str, row)))

# Sample input matrices (3x3)
first_matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
second_matrix = [[9, 8, 7], [6, 5, 4], [3, 2, 1]]

# Call the function to perform matrix multiplication
result_matrix = multiply_matrices(first_matrix, second_matrix)

# Display the matrices
print("First Matrix:")
display_matrix(first_matrix)

print("\nSecond Matrix:")
display_matrix(second_matrix)

print("\nResult Matrix:")
display_matrix(result_matrix)

Testing the Program

Feel free to replace the sample matrices with your own 3x3 matrices in the main function to test the program with different input.

Output

First Matrix:
1   2   3
4   5   6
7   8   9

Second Matrix:
9   8   7
6   5   4
3   2   1

Result Matrix:
30   24   18
84   69   54
138  114  90

Run the program to see the result of the matrix multiplication.

How the Program Works

The program defines a function multiply_matrices that takes two matrices (first_matrix and second_matrix) and computes their product, storing the result in the result_matrix.
It initializes the result_matrix with zeros and uses three nested loops to perform the matrix multiplication.
The display_matrix function is used to display the contents of a matrix.
Sample input matrices (first_matrix and second_matrix) are provided, and the program calls the multiplication function.
The program then displays the original matrices and the result matrix.

Understanding the Concept of Matrix Multiplication

Matrix multiplication is defined as follows: given two matrices A (of dimensions m x n) and B (of dimensions n x p), the product matrix C (of dimensions m x p) is obtained by multiplying each element of a row in matrix A by the corresponding element of a column in matrix B and summing up the results.

Conclusion

Matrix multiplication is a powerful operation used in various fields, including graphics, physics simulations, and machine learning.

Understanding the logic behind matrix multiplication and implementing it in python provides a foundational understanding of linear algebra in computer science.

Feel free to experiment with different matrix sizes and values to further explore the capabilities of this program. Happy coding!