What algebraic properties do bivectors have? They have the same operations that vectors have, so do they form a linear space? This video answers that question and looks at some of the consequences.
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
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Jason Killian
jerrud
Richard Penner
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Sections:
00:00 Introduction
00:38 Linear Space Review
01:57 Negative Bivectors
02:09 Zero Bivector
02:32 Dimension Issues
03:15 2D Trick
04:54 3D Trick
06:10 Commutativity
07:13 Distributivity
08:08 Triangle Inequality
08:51 Associativity
11:50 Bivectors Form a Linear Space
12:24 2D Bivector Basis
13:41 3D Bivector Basis
14:52 Bivector Calculations/Exercise
15:27 Bivector Magnitude
16:56 Conclusion