Tools

Eigen values, eigen vectors and diagonalization

  1. Click on the “Multiples of x∈R2” button to see the geometry of multiples of elements of R2.
  2. Click on the “T(x) ∈R2” button to visualize the role of T.
  3. To see the combined view of multiples of X∈R2 and T(x) ∈R2, click on the “Combined View” button.
  4. To understand eigenvalue and eigenvector, click on the “Visualization (Eigenvalue and Eigenvector)” button.
  5. Click on the “Next” Button to go to the next page.
  6. Enter the values of a, c and d to choose matrix A and click on “Submit” button to display the matrix A.
  7. Click on the “Eigenvalues” button to learn the working of eigenvalues through characteristic equation and its roots.
  8. Click on “Eigenvector” button to learn the working of eigenvectors through solutions of equations.
  9. Click on “Next” button to go to the next page.
  10. Observe the transformation defined and click on “Eigenvalues” button to see the eigenvalues of the transformation along with the justification.
  11. Click on the “Eigenvectors” button to see the eigenvectors corresponding to the displayed eigenvalues.
  12. Study the “Visualization” section to understand the geometric interpretation of the transformation T and its eigenvalues and eigenvectors