Uploaded August 2025 | Updated September 2026, 3 weeks ago
What is a change of basis—and why does it matter in real life? In this video, we break down the concept of change of basis in linear algebra using real-world examples: why RGB doesn’t work for printers, how clothing manufacturers design better-fitting shirts, and how body measurements relate to principal component analysis (PCA). With visuals, 3D plots, and simple vector math, we make abstract ideas concrete and intuitive. Perfect for students learning linear algebra, math educators, or anyone curious how math shapes the world. If you’ve ever struggled with understanding coordinate transformations or PCA, this is the change of basis explanation you’ve been waiting for.
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
Homogeneous Coordinates: youtu.be/x1F4eFN_cos
Audio Compression: youtu.be/eQT3qT85IyU
Donate: donate.churchofjesuschrist.org/contribute/byu/physical-mathematical-sciences/math-education
Instagram: instagram.com/maththeworld
Twitter/X: twitter.com/math_the_world
Facebook: facebook.com/maththeworldproject
Email: MathTheWorld@byu.edu
Created by Doug Corey
Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media
© 2025 BYU
What is a change of basis—and why does it matter in real life? In this video, we break down the concept of change of basis in linear algebra using real-world examples: why RGB doesn’t work for printers, how clothing manufacturers design better-fitting shirts, and how body measurements relate to principal component analysis (PCA). With visuals, 3D plots, and simple vector math, we make abstract ideas concrete and intuitive. Perfect for students learning linear algebra, math educators, or anyone curious how math shapes the world. If you’ve ever struggled with understanding coordinate transformations or PCA, this is the change of basis explanation you’ve been waiting for.
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
Homogeneous Coordinates: youtu.be/x1F4eFN_cos
Audio Compression: youtu.be/eQT3qT85IyU
Donate: donate.churchofjesuschrist.org/contribute/byu/physical-mathematical-sciences/math-education
Instagram: instagram.com/maththeworld
Twitter/X: twitter.com/math_the_world
Facebook: facebook.com/maththeworldproject
Email: MathTheWorld@byu.edu
Created by Doug Corey
Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media
© 2025 BYU
