Singular value decomposition (svd) in MATLAB - Mini Project: Build & Apply

Singular value decomposition (svd)

📖 Scenario: You work as a data analyst and want to understand the structure of a matrix representing some data. Singular value decomposition (SVD) helps break down the matrix into simpler parts.

🎯 Goal: Learn how to perform singular value decomposition on a matrix in MATLAB and display the decomposed matrices.

📋 What You'll Learn

Create a matrix variable named A with exact values

Create a variable k to select the number of singular values

Use MATLAB's svd function to decompose the matrix A

Display the matrices U, S, and V from the decomposition

💡 Why This Matters

🌍 Real World

Singular value decomposition is used in image compression, noise reduction, and data analysis to simplify complex data.

💼 Career

Understanding SVD is important for data scientists, engineers, and researchers working with large datasets and machine learning.

1

Create the matrix A

Create a 3x3 matrix called A with these exact values: first row [1 2 3], second row [4 5 6], third row [7 8 9].

MATLAB

% Create the matrix A with the specified values
% Your code here

Need a hint?

Use square brackets and semicolons to create rows in MATLAB.

2

Set the number of singular values k

Create a variable called k and set it to 2 to select the first two singular values.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
% Create the variable k and set it to 2
% Your code here

Need a hint?

Just assign the number 2 to the variable k.

3

Perform singular value decomposition

Use the MATLAB svd function to decompose matrix A into U, S, and V. Write [U, S, V] = svd(A);.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
k = 2;
% Perform SVD on A to get U, S, and V
% Your code here

Need a hint?

Use square brackets to capture multiple outputs from svd.

4

Display the matrices U, S, and V

Use disp to print the matrices U, S, and V in order.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
k = 2;
[U, S, V] = svd(A);
% Display U, S, and V matrices
% Your code here

Need a hint?

Use disp('Matrix U:') before displaying U to label the output.