Linear Algebra - What are Column Space and Kernel? | Linear Algebra Basics

What are the column space and the kernel of a matrix, and what do they tell us about how a matrix behaves? In this video, we look at matrices from a new perspective: as linear functions that map vectors from one space to another. You'll see how the column space captures all the outputs a matrix can produce, and how the kernel captures the directions that collapse to zero. 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 0:36 Matrices as Linear Functions 1:15 Linear Function Example 2:49 Introducing the Visualisation 3:25 The Column Space 4:53 Rank (Number of Independent Directions) 5:38 Column Space Examples 7:27 The Kernel / Null Space 8:35 Kernel Examples 11:28 Summary 12:12 Teaser: Rank–Nullity Theorem