Eigenvectors & Ellipses

Adjust the symmetric matrix A. Watch how it transforms the unit circle into an ellipse. The eigenvectors s1 and s2 scale to become the principal axes!

a11 (Top-Left) 1.25
a12 = a21 (Off-Diagonal) -0.43
a22 (Bottom-Right) 0.75

Live Eigenanalysis

A =
1.25 -0.43
-0.43 0.75
λ1 = 0.00, λ1s1 =
0.00 0.00
λ2 = 0.00, λ2s2 =
0.00 0.00

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Linear Algebra for Computer Science
Grid: 0.5 units / line
Unit Circle
Transformed Ellipse
Columns a₁, a₂
Principal Axis 1
Principal Axis 2