Eigenvectors Calculator

How to Use the Eigenvectors Calculator

This guide will walk you through using the Eigenvectors Calculator to find eigenvalues, eigenvectors, the determinant, and the trace of a matrix. The calculator supports both 2×2 and 3×3 matrices.

Step 1: Select Matrix Size

1. Select the matrix size from the dropdown labeled Matrix Size. You can choose either a 2×2 matrix or a 3×3 matrix. This choice determines the fields that are required for the next steps.

Step 2: Enter Matrix Elements

1. For a 2×2 matrix, enter the elements in the following fields:

   • Matrix Element (1,1) (labeled as a11)
   • Matrix Element (1,2) (labeled as a12)
   • Matrix Element (2,1) (labeled as a21)
   • Matrix Element (2,2) (labeled as a22)

2. For a 3×3 matrix, in addition to the above elements, enter the following elements:

   • Matrix Element (1,3) (labeled as a13)
   • Matrix Element (2,3) (labeled as a23)
   • Matrix Element (3,1) (labeled as a31)
   • Matrix Element (3,2) (labeled as a32)
   • Matrix Element (3,3) (labeled as a33)

3. Each field requires a numerical input. Ensure all required fields are filled to perform calculations.

Step 3: Calculate Results

Once all the necessary matrix elements have been entered, the calculator will compute the following:

• First Eigenvalue (λ₁): Calculated using a specific formula involving matrix elements.
• Second Eigenvalue (λ₂): Also calculated using a specific formula with the matrix elements.
• First Eigenvector Components: Includes x-component (v₁x) and y-component (v₁y).
• Second Eigenvector Components: Includes x-component (v₂x) and y-component (v₂y).
• Matrix Determinant: Calculated as the difference a11 * a22 – a12 * a21 for a 2×2 matrix.
• Matrix Trace: Sum of diagonals a11 + a22 for a 2×2 matrix.

The calculated results will be displayed with up to four decimal places for accuracy.