# Singular Value Decomposition Demo

This is a quick demo of what Singular Value Decomposition does. The math is based on notes from Data Mining and Engineering.

## Math

Starting with data \( X \) of size \( D \times N \), which represents \( N \) examples of \( D \)-dimensional data, if I run SVD on it and ask for \( K \) dimensions, SVD will decompose it into

where \( S \) is a diagonal matrix of size \( K \times K \), \( U \) and \( V \) are orthonormal matrices, and if \( X \) of size \( D \times N \), then \( U \) is size \( D \times K \) and \( V \) is of size \( K \times N \).