Eigenvector Calculator

How to Use the Eigenvector Calculator

This guide will walk you through the steps to use the Eigenvector Calculator to determine the eigenvalues and eigenvectors of a given matrix.

Step 1: Select the Matrix Dimension

Begin by selecting the dimension of your matrix:

• 2×2 Matrix: If you are working with a matrix that has 2 rows and 2 columns, select this option.
• 3×3 Matrix: Choose this option if you will be inputting a matrix with 3 rows and 3 columns. Keep in mind that this feature may not be fully configured in this calculator version.

This selection specifies the size of the matrix that you will input and adjusts the available fields accordingly.

Step 2: Enter Matrix Elements

Once you have selected the matrix dimension, you will need to input the elements of the matrix.

• For a 2×2 Matrix:
  • a11: Enter the value for the element in the first row and first column.
  • a12: Enter the value for the element in the first row and second column.
  • a21: Enter the value for the element in the second row and first column.
  • a22: Enter the value for the element in the second row and second column.
• For a 3×3 Matrix (additional fields, but optional in this version):
  • a13, a23: Values for elements in the first and second rows, third column.
  • a31, a32, a33: Values for the elements in the third row.

Ensure all required fields are filled with appropriate numerical values, following the given step increments.

Step 3: Calculate the Eigenvalues and Eigenvectors

After inputting all required data for the matrix, the calculator will compute the eigenvalues and eigenvectors automatically using the predetermined calculation logic.

• First Eigenvalue (λ₁): This value is computed using a formula that involves matrix elements and mathematical operations.
• Second Eigenvalue (λ₂): Similarly, calculated using another specific formula based on matrix input.
• Eigenvectors:
  • The x and y components of the first eigenvector, v₁, are derived using predetermined calculations linked to the matrix elements.
  • The x and y components of the second eigenvector, v₂, follow similar predefined logic.

The results will be presented with precision up to four decimal places.

Step 4: Review Your Results

Examine the eigenvalues and eigenvector components displayed in the result fields.

• Double-check your input data: If the results seem inaccurate, ensure the correct values were plugged into the input fields.
• Interpret the results: The eigenvalues and eigenvectors provide insight into the properties of the original matrix. They are essential components in many mathematical and engineering applications.

With these steps, you should be able to navigate the Eigenvector Calculator efficiently and extract valuable information from your matrix data.