# Singular Value Decomposition Part 2: Theorem, Proof, Algorithm

DevFeed: [Singular Value Decomposition Part 2: Theorem, Proof, Algorithm](<https://devfeed.tech/articles/singular-value-decomposition-part-2-theorem-proof-algorithm-40399.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2016/05/16/singular-value-decomposition-part-2-theorem-proof-algorithm/>)

Published: 2016-05-16T08:00:19Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [data](<https://devfeed.tech/topics/data.md>), [Code](<https://devfeed.tech/topics/code.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [code](<https://devfeed.tech/tags/code.md>), [data](<https://devfeed.tech/tags/data.md>), [examples](<https://devfeed.tech/tags/examples.md>), [github](<https://devfeed.tech/tags/github.md>), [github-repository](<https://devfeed.tech/tags/github-repository.md>), [greedy-algorithm](<https://devfeed.tech/tags/greedy-algorithm.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [singular-value-decomposition](<https://devfeed.tech/tags/singular-value-decomposition.md>)

## AI overview

This tutorial develops the mathematical foundations of singular value decomposition through definitions, proofs, and an algorithm. It explains best-approximating k-dimensional linear subspaces, vector projection, and squared distance, and mentions testing the method on a thousand-story CNN news dataset with accompanying code and examples in a GitHub repository.

## Source excerpt

I'm just going to jump right into the definitions and rigor, so if you haven't read the previous post motivating the singular value decomposition, go back and do that first. This post will be theorem, proof, algorithm, data. The data set we test on is a thousand-story CNN news data set. All of the data, code, and examples used in this post is in a github repository, as usual. We start with the best-approximating $ k$-dimensional linear subspace.