Vectors Are Not Lists of Numbers (Part 2) - From Zero to Geo 1.9

In this video, we explore the idea of linear spaces, where we generalize everything that we have learned in this chapter to a more abstract context. This topic is very useful in geometric algebra and beyond. We explore several examples of linear spaces and discuss why we care about them in geometric algebra. This video is a part of "From Zero to Geo", a series where we formulate geometric algebra, an incredibly powerful branch of mathematics, from the ground up. Full playlist here: https://www.youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy Here's the bonus video mentioned partway through: https://www.youtube.com/watch?v=T0b8-NJH79s Next video here: https://www.youtube.com/watch?v=_WWoG7sSBTo Discord: https://discord.gg/3Zj59zA2Rg Patreon: https://www.patreon.com/sudgylacmoe Patreon Supporters: AxisAngles Christoph Kovacs David Johnston p11 Richard Penner Rosario Sections: 00:00 Introduction 00:37 What is a vector? 03:11 Arrows 03:30 Numbers 04:12 Lists of numbers 05:34 2D Lines 07:01 Functions 08:27 Why do we care? 10:21 Conclusion