Singular Value Decomposition

Singular Value Decomposition Singular Value Decomposition (SVD) decomposes a matrix as $$ A = U \Sigma V^T $$\[ A = U \Sigma V^T \]Geometric Interpretation SVD can be understood as three transformations: Rotate the input space. Scale along orthogonal axes. Rotate into the output space.

September 29, 2026 · 1 min