2D SVD Visualization

Visualize how the Singular Value Decomposition breaks any 2×2 matrix into three geometric steps: rotate (V^T), scale (Σ), rotate (U). See rank deficiency collapse objects to a line.

Matrix A (2×2)

Enter matrix entries

[

]

Set as rotation matrix

Object & Display

Object shape

Show transformed grid

Show original (ghost)

Show basis vectors

Unit circle → ellipse

Show σ axes on ellipse

Animation

Visualize

Animates each SVD step: first rotation, scaling, second rotation.

Resets the animation and restores the original view.

Animates the full matrix transformation in one smooth motion.

Speed

1.0×

Preset:

e₁

e₂

Ellipse

σ₁

σ₂

Ghost

SVD Decomposition

Determinant & Singular Values

Decomposition Steps

Step 1: First Rotation

Apply V^T — rotate to align with singular directions

Step 2: Scaling

Apply Σ — stretch/compress along axes by σ₁, σ₂

Step 3: Second Rotation

Apply U — rotate to final orientation