Singular Value Decomposition

A = UΣVᵀ — every linear map is a rotation, a stretch, then another rotation. Watch the unit sphere transform.

A
×
Presets
Singular values
σ1 = 2σ2 = 1σ3 = 0.5
condition κ = 4
rank ≈ 3
‖A‖₂ = 2
Stage
interp t1.00
Decomposition
Σ
[200010000.5]\begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0.5 \end{bmatrix}