Eigenvalue and Eigenvector Calculator

Description

This MATLAB program is designed to calculate eigenvalues and eigenvectors of a square matrix provided by the user. Eigenvalues and eigenvectors are fundamental concepts in linear algebra and have various applications in mathematics, science, and engineering.

How to Use

1. Make sure your input matrix is square, meaning it has the same number of rows and columns (N x N).
2. Input your matrix using square brackets and semicolons to separate rows. Here's an example for a 2x2 matrix:

   [3 0; 8 -1]
           

   And for a 3x3 matrix:

   [0 0 -2; 1 2 1; 1 0 3]
           

How It Works

1. The program starts by taking the user's input for the matrix.
2. It then converts the input into a MATLAB symbolic matrix for calculations.
3. The program verifies if the input matrix is square (m x n must be the same).
4. Eigenvalues and eigenvectors are calculated using built-in MATLAB functions.
5. The results are displayed, showing the eigenvalues and their corresponding eigenvectors.

Output

The eigenvalues are shown as a list.

For each eigenvalue, the corresponding eigenvector is displayed.

Note

• Eigenvalues represent how a matrix scales eigenvectors, and they have applications in various fields, including physics and engineering.
• Eigenvectors are the directions that remain unchanged when transformed by the matrix.

Enjoy using this MATLAB program for eigenvalue and eigenvector calculations!