Linear Algebra - What is a Change of Basis? | Linear Algebra Basics

Learn how to perform a change of basis in this Linear Algebra Basics lesson. We explore coordinate systems, basis vectors, and how to find the transition matrix from the ground up. In this video, we build the concept of a change of basis by looking at how the same vector can have different coordinate descriptions. You will see how to move between systems using matrices, how to combine these changes, and why the right basis can make complex transformations much simpler. Check out my full Linear Algebra playlist here: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm 📌 Timestamps: 0:00 Introduction 1:35 What is a Basis? (Quick Recap) 2:56 Moving Between Coordinate Systems 3:48 Change of Basis Matrix 7:09 Combining Basis Changes 8:43 Why Some Bases Are More Useful #linearalgebra #mathtutorial #changeofbasis