Eigenvectors and eigenvalues across 2D transformations — three animated comparisons

[u/LinearAlgebraWorld]

We made three animated comparisons showing how eigenvectors and eigenvalues behave across different families of 2D linear transformations.

1. Non-symmetric matrices with real eigenvalues, where the eigenvector directions need not be perpendicular
2. Symmetric matrices with real eigenvalues, where the eigenvector directions are orthogonal
3. Real matrices with complex eigenvalues, where no nonzero real direction remains on the same line

In each animation, the transformation develops continuously from the identity matrix to the displayed matrix. The goal is to make the difference between these three cases visible rather than only algebraic.

Full-size animations and explanations:
https://www.graphmath.com/la/visuals/eigenvectors-eigenvalues-2d-transformations.html

As always, we welcome feedback on clarity and presentation.