sudgylacmoe | Vectors Are Not Lists of Numbers (Part 2) - From Zero to Geo 1.9 @sudgylacmoe | Uploaded December 2022 | Updated October 2024, 4 hours ago.
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: youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy
Here's the bonus video mentioned partway through: youtube.com/watch?v=T0b8-NJH79s
Next video here: youtube.com/watch?v=_WWoG7sSBTo

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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