3D Eigen Explorer

Grab the colored handles to rotate an eigenvector. The matrix A = QΛQᵀ rebuilds instantly — watch the ellipsoid and vector field reshape.

drag the colored spheres · scroll = zoom · right-drag = pan
Eigenvalues
λ1 (v₁)2
λ2 (v₂)1
λ3 (v₃)0.5
Reconstructed A
A=[200010000.5]A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0.5 \end{bmatrix}
A = QΛQᵀ — symmetric by construction.
What you're seeing

The faint gray sphere is the unit ball. The orange surface is its image under A — an ellipsoid with semi-axes |λᵢ| along the eigenvectors.

Each thin gray segment connects a sample point v to Av. Along the colored axes the segment stays colinear — that's the defining property of an eigenvector.

A negative λ flips the corresponding axis through the origin.