Singular Value Decomposition (SVD)
March 18, 2026Singular Value Decomposition (SVD) #
Singular Value Decomposition (SVD) is one of the most important matrix decomposition techniques in linear algebra and machine learning.
It factorises any matrix into three simpler matrices that reveal its structure.
Key Idea: SVD decomposes a matrix into rotations + scaling. It tells us how data is transformed along orthogonal directions.
Definition #
For any matrix in real space: \[ A \in \mathbb{R}^{m \times n} \]