Episode 62 - Tai-Danae Bradley — Kevin Knudson

Abstraction: Tai-Danae Bradley explains SVD and its parallel to category theory adjunction

Key points:

• Tai-Danae Bradley: postdoc at X (Google X), PhD from CUNY Graduate Center, runs math blog math3ma
• Favorite theorem: Singular Value Decomposition — any matrix can be factored as U Σ Vᵀ with no assumptions on the matrix
• SVD is not a "consolation prize" for non-square matrices; it is ubiquitous and fundamental across science and engineering
• Connection to category theory: formal concept analysis (object-feature relations) is analogous to eigenvectors via adjunction, making SVD a template that maps to categorical constructions (a "Mad Libs" of math)
• Co-authored graduate text "Topology: A Categorical Approach" with John Terilla and Tyler Bryson

Connections: Tai Danae Bradley · Google X · Singular Value Decomposition · Category Theory · Linear Algebra

Source: https://kpknudson.com/my-favorite-theorem/2021/1/15/episode-62-tai-danae-bradley