Visualizing Singular Value Decomposition (SVD), 4 different ways

A visual and intuitive explanation of Singular Value Decomposition (SVD).

In this video, we build SVD from a geometric perspective—starting from how matrices transform vectors, and gradually connecting this to change of basis, principal component analysis (PCA), and low-rank approximation.

The goal is to make SVD feel natural and inevitable, not mysterious.

Timestamps:
00:00 Vector transformation
06:43 Change of basis
09:45 PCA
16:35 Low-rank approximation

Topics covered:
- Singular Value Decomposition (SVD)
- Geometric interpretation of matrices
- Change of basis
- Principal Component Analysis (PCA)
- Low-rank approximation

Видео Visualizing Singular Value Decomposition (SVD), 4 different ways канала Jingyuan Hu