sudgylacmoe | Describing Many Vectors With a Few - From Zero to Geo 1.6 @sudgylacmoe | Uploaded January 2022 | Updated October 2024, 2 hours ago.
While we learned in the last video how to describe spaces with vectors, it can be helpful to be able to describe spaces with just a few vectors. In this video, we explore how to do this. This leads us to consider the important ideas of linear combinations and spans.
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=rZXen-HX7dA
Discord: discord.gg/3Zj59zA2Rg
Patreon: patreon.com/sudgylacmoe
Patreon Supporters:
AxisAngles
Bill Six
Richard Penner
Sections:
00:00 Introduction
00:26 Span of x hat
01:02 Span of x hat and y hat
03:42 Span of x hat, y hat, and z hat
04:05 Span of non-perpendicular vectors
05:01 Span of two parallel vectors
05:35 Linear combinations
06:28 Span
08:13 Is the span a space?
10:36 Final answer
While we learned in the last video how to describe spaces with vectors, it can be helpful to be able to describe spaces with just a few vectors. In this video, we explore how to do this. This leads us to consider the important ideas of linear combinations and spans.
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=rZXen-HX7dA
Discord: discord.gg/3Zj59zA2Rg
Patreon: patreon.com/sudgylacmoe
Patreon Supporters:
AxisAngles
Bill Six
Richard Penner
Sections:
00:00 Introduction
00:26 Span of x hat
01:02 Span of x hat and y hat
03:42 Span of x hat, y hat, and z hat
04:05 Span of non-perpendicular vectors
05:01 Span of two parallel vectors
05:35 Linear combinations
06:28 Span
08:13 Is the span a space?
10:36 Final answer
