Animated transformation, eigenvectors & geometric visualization
A 2×2 matrix represents a linear transformation: rotation, scaling, reflection, shearing. The determinant tells area scaling (det=0 collapses space). Eigenvectors are directions unchanged by the transformation — they only get scaled by the eigenvalue. Toggle Eigenvectors to see them, Transform Grid to see the full plane transformation, or Animate to watch the unit square smoothly morph.