# singular value decomposition

Published articles for singular value decomposition.

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## 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.

## Singular Value Decomposition Part 1: Perspectives on Linear Algebra

DevFeed: [Singular Value Decomposition Part 1: Perspectives on Linear Algebra](<https://devfeed.tech/articles/singular-value-decomposition-part-1-perspectives-on-linear-algebra-40398.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2016/04/18/singular-value-decomposition-part-1-perspectives-on-linear-algebra/>)

Published: 2016-04-18T09:00:40Z

Content type: article

Language: en

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

Topics: [Data analysis](<https://devfeed.tech/topics/data-analysis.md>), [Computer science](<https://devfeed.tech/topics/computer-science.md>), [Statistics](<https://devfeed.tech/topics/statistics.md>), [Optimization](<https://devfeed.tech/topics/optimization.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [data-analysis](<https://devfeed.tech/tags/data-analysis.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [regression](<https://devfeed.tech/tags/regression.md>), [singular-value-decomposition](<https://devfeed.tech/tags/singular-value-decomposition.md>), [statistics](<https://devfeed.tech/tags/statistics.md>)

### AI overview

This first post in a two-part series motivates and introduces singular value decomposition (SVD). It explains how matrices can represent both linear transformations and organized data, and outlines the role of SVD in applications such as regression, prediction, and approximate optimization solutions.

### Source excerpt

The singular value decomposition (SVD) of a matrix is a fundamental tool in computer science, data analysis, and statistics. It's used for all kinds of applications from regression to prediction, to finding approximate solutions to optimization problems. In this series of two posts we'll motivate, define, compute, and use the singular value decomposition to analyze some data. (Jump to the second post) I want to spend the first post entirely on motivation and background.