What Eigenvectors Really Do
This animation shows how a matrix transforms vectors across the plane, stretching and rotating most of them, while eigenvectors alone keep their original direction, only scaling by a factor called the eigenvalue. Grid lines warp under the transformation, highlighting the special directions that stay fixed. Useful for students in linear algebra learning why eigenvectors matter for understanding matrix behavior, diagonalization, and applications like stability analysis.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Explain how eigenvectors work
Make the next one in this series
- Show how to compute eigenvalues using the characteristic polynomial step by step
- Visualize diagonalization of a matrix using its eigenvectors and eigenvalues
- Demonstrate complex eigenvalues and what they mean geometrically as rotation
