Singular Value Decomposition at FIFA 2022

TL;DR

This paper provides an intuitive, applied explanation of singular value and polar decompositions using FIFA 2022 World Cup data, aimed at engaging students in linear algebra concepts.

Contribution

It introduces a practical, engaging approach to teaching SVD and polar decomposition through FIFA tournament analysis, suitable for classroom or take-home projects.

Findings

Enhanced understanding of SVD in real-world contexts

Student engagement through sports data analysis

Insights into interpreting singular vectors in tournament data

Abstract

The singular value decomposition is arguably one of the most fundamental results in linear algebra. While rigorous proof of this result is of importance, equally important is the motivation in the applied settings. We provide a lively and quite intuitive presentation on the appearance of the singular value decomposition of a matrix in the round robin tournaments, as well as the polar decomposition, all in the context of FIFA 2022 World Cup. This exposition is intended to be implemented in a class setting or given as a take home project in the second linear algebra course. Given the popularity of this world event we expect students to be interested and engaged throughout the analysis and ensuing conversations. Discussions among students should be enriching as they attempt to analyse the various FIFA groups and give comparisons. Furthermore, ideas in regards how to best interpret the singular vectors should be quite interesting. Basic notions and results from the first year linear algebra course are assumed.