sudgylacmoe | Superior Spanning Sets - From Zero to Geo 1.7 @sudgylacmoe | Uploaded April 2022 | Updated October 2024, 2 hours ago.
Some spanning sets are better than others. But what are the properties that make one spanning sets better than another one? In this video, we focus on one important property that vectors can have: linear independence.

This video was a pain to make! It took me a long time to find a way to describe linear dependence/independence in a way that felt intuitive to me. I hope that the video was worth the wait.

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
Next video here: youtube.com/watch?v=OjbP2Ki-8RY

Discord: discord.gg/3Zj59zA2Rg

Patreon: patreon.com/sudgylacmoe

Patreon Supporters:
AxisAngles
Bill Six
Richard Penner
Rosario

Sections:
00:00 Introduction
00:55 Definition of Linear Dependence
01:50 Linear Dependence Exercise
03:43 Special Cases of Determining Linear Dependence
05:27 Alternate Definitions of Linear Dependence
09:01 Fundamental Concept
09:29 Bases
10:47 Conclusion