Linear Algebra - What are Linear Transformations? | Linear Algebra Basics

What are linear transformations, and how do they change entire spaces? In this video, we build an intuitive understanding of linear maps (also known as linear transformations) in linear algebra. You will see how matrices act as functions that stretch, rotate, or collapse space, and why everything is determined by what happens to the basis vectors. This video is slightly longer than usual to give you a deeper geometric intuition. If you enjoyed this video, check out the full playlist on linear algebra basics: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm 📌 Timestamps: 0:00 Introduction 0:37 Vector Spaces 3:01 What Makes a Mapping Linear? 5:47 Matrices as Linear Transformations 7:29 Examples of Linear Transformations 9:50 Understanding Linear Maps via Basis Vectors 14:04 Collapsing Dimensions and the Null Space