np.linalg.eig() for eigenvalues in NumPy - Mini Project: Build & Apply

Finding Eigenvalues and Eigenvectors with np.linalg.eig()

📖 Scenario: Imagine you are analyzing a simple system where you want to understand its main directions of change. This is common in physics, engineering, and data science. Eigenvalues and eigenvectors help us find these directions.

🎯 Goal: You will create a matrix, use np.linalg.eig() to find its eigenvalues and eigenvectors, and then display the results.

📋 What You'll Learn

Create a 2x2 numpy array called matrix with values [[4, 2], [1, 3]]

Create a variable called eigenvalues and a variable called eigenvectors to store the results of np.linalg.eig(matrix)

Print the eigenvalues and eigenvectors variables

💡 Why This Matters

🌍 Real World

Eigenvalues and eigenvectors help in physics to understand vibrations, in data science for principal component analysis, and in engineering for system stability.

💼 Career

Many data science and engineering jobs require understanding matrix properties and using eigenvalues for dimensionality reduction and system analysis.

1

Create the matrix

Create a 2x2 numpy array called matrix with these exact values: [[4, 2], [1, 3]]

NumPy

import numpy as np
# Create the matrix variable here
# Your code here

Need a hint?

Use np.array() to create the matrix with the given values.

2

Calculate eigenvalues and eigenvectors

Use np.linalg.eig() on the matrix to get eigenvalues and eigenvectors. Store them in variables called eigenvalues and eigenvectors respectively.

NumPy

import numpy as np
matrix = np.array([[4, 2], [1, 3]])
# Calculate eigenvalues and eigenvectors here
# Your code here

Need a hint?

Use eigenvalues, eigenvectors = np.linalg.eig(matrix) to get both results at once.

3

Print eigenvalues

Print the variable eigenvalues to display the eigenvalues of the matrix.

NumPy

import numpy as np
matrix = np.array([[4, 2], [1, 3]])
eigenvalues, eigenvectors = np.linalg.eig(matrix)
# Print eigenvalues here
# Your code here

Need a hint?

Use print(eigenvalues) to show the eigenvalues.

4

Print eigenvectors

Print the variable eigenvectors to display the eigenvectors of the matrix.

NumPy

import numpy as np
matrix = np.array([[4, 2], [1, 3]])
eigenvalues, eigenvectors = np.linalg.eig(matrix)
print(eigenvalues)
# Print eigenvectors here
# Your code here

Need a hint?

Use print(eigenvectors) to show the eigenvectors.