How to Find Eigenvalues in MATLAB: Simple Guide

In MATLAB, you can find eigenvalues of a matrix using the eig function. Simply pass your square matrix to eig, and it returns a vector of eigenvalues.

Syntax

The basic syntax to find eigenvalues is:

• e = eig(A): Returns a column vector e containing the eigenvalues of the square matrix A.
• [V,D] = eig(A): Returns matrix V whose columns are eigenvectors and diagonal matrix D with eigenvalues on the diagonal.

matlab

e = eig(A);
[V,D] = eig(A);

Example

This example shows how to find eigenvalues of a 2x2 matrix and display them.

matlab

A = [4 2; 1 3];
e = eig(A);
disp('Eigenvalues:');
disp(e);

Output

Eigenvalues:
5.0000
2.0000

Common Pitfalls

Common mistakes include:

• Passing a non-square matrix to eig, which causes an error.
• Confusing eigenvalues with eigenvectors; eig returns eigenvalues by default unless you request eigenvectors.
• Not handling complex eigenvalues properly when the matrix is not symmetric.

matlab

A = [1 2 3; 4 5 6]; % Non-square matrix
% Wrong usage:
e = eig(A); % This will cause an error

% Correct usage:
A = [1 2; 3 4];
e = eig(A);

Output

Error using eig
Matrix must be square.

Quick Reference

Remember these tips when finding eigenvalues in MATLAB:

• Use eig(A) for eigenvalues only.
• Use [V,D] = eig(A) to get eigenvectors and eigenvalues.
• Matrix A must be square.
• Eigenvalues can be complex numbers.

Key Takeaways

Use the eig function to find eigenvalues of a square matrix in MATLAB.

Pass your matrix as eig(A) to get eigenvalues as a vector.

Request eigenvectors with [V,D] = eig(A) if needed.

Ensure the matrix is square to avoid errors.

Eigenvalues may be complex if the matrix is not symmetric.