SVD Explorer - Interactive Visualization

Singular Value Decomposition (SVD) is one of the most important matrix factorizations in machine learning. Every matrix A can be written as U·Σ·Vᵀ - a rotation, scaling, and another rotation. This visualization shows how a unit circle transforms through each stage: Vᵀ rotates it, Σ stretches it into an ellipse, and U rotates it again. The singular values σ₁ and σ₂ are the axes of that ellipse.

• Watch a unit circle transform into an ellipse through U, Σ, Vᵀ stages
• Adjust singular values σ₁ and σ₂ to control stretching
• See condition number κ = σ₁/σ₂ and its effect on stability
• Understand why SVD underlies PCA, LSA, and matrix completion
• See how rank and singular values relate to data structure

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.