## Introduction to Matrix Multiplication

Matrix multiplication is a fundamental operation in linear algebra and is widely used in various fields such as computer graphics, machine learning, and scientific computing. In the context of Numpy, a powerful numerical computing library in Python, matrix multiplication is efficiently performed using the dot() and matmul() functions. In this chapter, we will explore the basics of matrix multiplication, the differences between the dot() and matmul() functions, and their practical applications.

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### Code Snippet: Basic Matrix Multiplication

import numpy as np # Create two matrices matrix1 = np.array([[1, 2], [3, 4]]) matrix2 = np.array([[5, 6], [7, 8]]) # Perform matrix multiplication result = np.dot(matrix1, matrix2) # Print the result print(result)

Output:

[[19 22] [43 50]]

### Code Snippet: Multiplying Two 3×3 Matrices

import numpy as np # Create two 3x3 matrices matrix1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) matrix2 = np.array([[9, 8, 7], [6, 5, 4], [3, 2, 1]]) # Perform matrix multiplication result = np.dot(matrix1, matrix2) # Print the result print(result)

Output:

[[ 30 24 18] [ 84 69 54] [138 114 90]]

## Setting Up the Numpy Environment

Before we dive into matrix multiplication in Numpy, let’s set up our environment by installing Numpy and importing the library. Numpy can be easily installed using pip, the Python package installer, by running the following command:

pip install numpy

Once Numpy is installed, we can import it into our Python script using the following line of code:

import numpy as np

With Numpy successfully installed and imported, we are now ready to perform matrix multiplication using its powerful functions.

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### Code Snippet: Using the dot() Function for Matrix Multiplication

import numpy as np # Create two matrices matrix1 = np.array([[1, 2], [3, 4]]) matrix2 = np.array([[5, 6], [7, 8]]) # Perform matrix multiplication using the dot() function result = np.dot(matrix1, matrix2) # Print the result print(result)

Output:

[[19 22] [43 50]]

### Code Snippet: Using the matmul() Function for Matrix Multiplication

import numpy as np # Create two matrices matrix1 = np.array([[1, 2], [3, 4]]) matrix2 = np.array([[5, 6], [7, 8]]) # Perform matrix multiplication using the matmul() function result = np.matmul(matrix1, matrix2) # Print the result print(result)

Output:

[[19 22] [43 50]]

(Note: The code snippets in this article assume that Numpy has been properly installed and imported in the Python environment.)