Singular Value Decomposition (SVD)

Wed, 18 Mar 2026 00:00:00 +0000

Singular 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.

For any matrix in real space: \[ A \in \mathbb{R}^{m \times n} \]