Singular Value Decomposition

A = UΣVT — how A maps the unit circle in ℝ²

Right singular vectors (V)
Left singular vectors (U)
Singular values
Matrix A
Samples
Input space — right singular vectors (V)
Output space — image of unit circle
Singular values
Legend
v₁ (input) → σ₁u₁ (output)
v₂ (input) → σ₂u₂ (output)
unit circle / image ellipse
click to probe x → Ax
samples (input)
samples (output)