Singular value decomposition (SVD) is a popular method of matrix decomposition that reduces a complex matrix into its constituent parts so that subsequent matrix calculations are simpler.

The general equation for SVD for real-valued matrices is:

**A = U * Σ * V^T**

Where *A* represents the real m x n matrix that is being decomposed, *U* is a m x m matrix, *Σ* is an m x n diagonal matrix, and *V^T (i.e. V transposed) *is the transpose of an n x n matrix.

The columns of the *U *matrix are called the left-singular vectors of matrix *A*, while the columns of the *V *matrix are called the right-singular vectors of *A*. The diagonal values of the *Σ *matrix are the singular values of matrix *A*.

### Singular Value Decomposition in Machine Learning

SVD is a commonly used method for data reduction in machine learning, particularly in unsupervised learning algorithms. It's one of the core elements of the recommender systems of international companies like Google, Facebook, Netflix and Youtube, helping them determine the order that pages appear in search results, what content and ads you see, and what shows / movies / videos you might enjoy.

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## Further reading

A Gentle Introduction to Singular-Value Decomposition for Machine Learning

Jason Brownlee

Web

Foundations of Machine Learning : Singular Value Decomposition (SVD)

Patrick Luboobi

Web

Singular Value Decomposition (SVD) tutorial

MIT

Web

## Documentaries, videos and podcasts

Singular Value Decomposition (SVD) - MIT OpenCourseWare

May 6th, 2016