Singular Value Decomposition
A = UΣV
T
— how A maps the unit circle in ℝ²
Right singular vectors (V)
θ
V
0.00
rad
Left singular vectors (U)
θ
U
1.05
rad
Singular values
σ₁
2.00
σ₂
0.80
Matrix A
Samples
+ 50
+ 200
Clear
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)