Using NumPy to Generate Identity and Diagonal Matrices

In this tutorial, we are going to learn and understand: Using NumPy to Generate Identity and Diagonal Matrices.

Introduction

Matrices play an important role in various mathematical and computational applications. In this tutorial, we will learn how to use NumPy to generate identity and diagonal matrices.

Why use Identity and Diagonal Matrices

Identity and Diagonal matrices are widely used in various places in linear algebra and machine learning situations. Some applications include:

Maintaining matrix properties during transformations
Simplifying computations in algorithms
Using them as special cases in various mathematical models

Now, let’s see how to implement these matrices using the NumPy library in Python.

Step 1: Import Required Libraries

We first need to import NumPy library, for the required matrix operations.

import numpy as np

Step 2: Generating Identity Matrix

An identity matrix is a square matrix filled with ones on the diagonal and filled with zeroes everywhere else. We can generate it by using user input, by asking the user for the size of the matrix.

identity_matrix = np.eye(int(input("Enter the size of the identity matrix: ")))

Step 3: Generating Diagonal Matrix

A diagonal matrix has specific values in its diagonal, and all other elements are filled with zeroes. Here, we can generate it by using user input, by asking the user for the elements.

diagonal_elements = eval(input("Enter the diagonal elements of the matrix as a list: "))
diagonal_matrix = np.diag(diagonal_elements)

Step 4: Displaying Results

Now after creating the matrices, we can print the results.

print("Identity Matrix:")
print(identity_matrix)
print("\nDiagonal Matrix:")
print(diagonal_matrix)

Output

Enter the size of the identity matrix: 3
Enter the diagonal elements of the matrix as a list: [1,2,3,4,5]
Identity Matrix:
[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

Diagonal Matrix:
[[1 0 0 0 0]
 [0 2 0 0 0]
 [0 0 3 0 0]
 [0 0 0 4 0]
 [0 0 0 0 5]]

Conclusion

In this tutorial, we have learned how to create identity and diagonal matrices using the NumPy python library. To recap:

Identity Matrix: Used in various transformations and linear equation solving situations.
Diagonal Matrix: Used in simplifying computations and for representation of linear equations.