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

Eigenvalues and eigenvectors (eig)

📖 Scenario: You are working as a data analyst and need to understand the properties of a matrix representing some data relationships. Eigenvalues and eigenvectors help you find important directions and strengths in the data.

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

📋 What You'll Learn

Create a 2x2 matrix with specific values

Define a variable to hold the matrix size

Use the eig function to find eigenvalues and eigenvectors

Display the eigenvalues and eigenvectors

💡 Why This Matters

🌍 Real World

Eigenvalues and eigenvectors are used in data analysis, physics, and engineering to understand system behaviors and transformations.

💼 Career

Knowing how to compute and interpret eigenvalues and eigenvectors is important for roles in data science, machine learning, and scientific computing.

1

Create the matrix

Create a 2x2 matrix called A with these exact values: 4, 2 in the first row and 1, 3 in the second row.

MATLAB

% Create the matrix A
% Your code here

Need a hint?

Use square brackets and semicolon to separate rows in MATLAB.

2

Define matrix size

Create a variable called n that stores the size of matrix A using the size function.

MATLAB

A = [4 2; 1 3];
% Define the size of matrix A
% Your code here

Need a hint?

Use size(A,1) to get the number of rows.

3

Calculate eigenvalues and eigenvectors

Use the eig function to calculate eigenvalues and eigenvectors of matrix A. Store eigenvectors in V and eigenvalues in D.

MATLAB

A = [4 2; 1 3];
n = size(A,1);
% Calculate eigenvalues and eigenvectors
% Your code here

Need a hint?

Use [V,D] = eig(A) to get eigenvectors and eigenvalues.

4

Display the results

Display the eigenvalues stored in D and eigenvectors stored in V using disp.

MATLAB

A = [4 2; 1 3];
n = size(A,1);
[V,D] = eig(A);
% Display eigenvalues and eigenvectors
% Your code here

Need a hint?

Use disp('Eigenvalues:') and disp(D) to show eigenvalues, similarly for eigenvectors.