Eigenvalues and eigenvectors (eig) in SciPy - Mini Project: Build & Apply

Finding Eigenvalues and Eigenvectors with SciPy

📖 Scenario: You work as a data analyst for a company that studies vibrations in mechanical systems. You need to find the natural vibration modes of a system represented by a matrix.

🎯 Goal: Learn how to calculate eigenvalues and eigenvectors of a matrix using SciPy's eig function.

📋 What You'll Learn

Create a 2x2 matrix as a NumPy array

Import the eig function from scipy.linalg

Use eig to find eigenvalues and eigenvectors

Print the eigenvalues and eigenvectors

💡 Why This Matters

🌍 Real World

Eigenvalues and eigenvectors help engineers understand how structures vibrate and respond to forces.

💼 Career

Data scientists and engineers use eigen decomposition in signal processing, principal component analysis, and system stability analysis.

1

Create the matrix

Create a variable called matrix and set it to a 2x2 NumPy array with values [[4, 2], [1, 3]].

SciPy

import numpy as np
# Create the matrix variable as a 2x2 NumPy array
# Your code here

Need a hint?

Use np.array to create the matrix with the exact values.

2

Import the eig function

Import the eig function from the scipy.linalg module.

SciPy

import numpy as np
matrix = np.array([[4, 2], [1, 3]])
# Import eig from scipy.linalg
# Your code here

Need a hint?

Use from scipy.linalg import eig to import the function.

3

Calculate eigenvalues and eigenvectors

Use the eig function with the variable matrix to calculate eigenvalues and eigenvectors. Store the results in variables called eigenvalues and eigenvectors.

SciPy

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

Need a hint?

Call eig(matrix) and unpack the result into eigenvalues and eigenvectors.

4

Print the eigenvalues and eigenvectors

Print the variables eigenvalues and eigenvectors to display the results.

SciPy

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

Need a hint?

Use two print statements, one for eigenvalues and one for eigenvectors.