Understanding Eigenvectors

Eigenvectors keep direction under transformation; only scaled by eigenvalues.

• Red & Cyan lines show eigenvector directions
• Drag orange vector on the left side to see how the transformation works.
• Drag orange vector along the eigenvector directions, and observe how the vector doesn't change direction once transformed -- it just scales
• Try different matrices to see changes
• Eigenvalues & matrix determine scaling, flipping, rotation

💡 Use preset buttons to explore classic examples!