Singular Value Decomposition (SVD) in 3D

Deconstructing a 3D transformation: A = U Σ Vᵀ

3D SVD Controls

Singular Values (σ)

Step 0: The Standard 3D Space

L: M = I
R: M = I

The original 3D unit sphere. The colored lines are the Right Singular Vectors (v₁, v₂, v₃). Drag to rotate the 3D view.

Direct Transformation (A)

Decomposition (U Σ Vᵀ)