The Fundamental Object of Geometric Algebra - From Zero to Geo 2.6

Up until this point, we have been looking at several different kinds of geometric objects, like vectors, bivectors, and in general, k-vectors. Is there some way to combine them? Answering this question leads to a discussion of multivectors, which are the fundamental object of geometric algebra.

Here is my previous video on direct sums:    • You can add scalars and vectors!  From Zer...  

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:    • From Zero to Geo  
Next video here:    • What do People Use Instead of Multivectors...  

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Sections:
00:00 Introduction
00:33 Definition of Multivectors
02:12 Practical Look at Multivectors
04:00 Algebraic Dimension of Multivectors
05:10 k-vectors Are Multivectors
05:45 Homogeneous Multivectors
06:14 All Zeros Are Equal
06:43 Notation for the Set of Multivectors
07:43 Grading
08:23 Grade Projection Operator
09:11 Exercise on the Grade Projection Operator
10:01 Conclusion

Corrections:
04:43 Sorry, up to (n choose n), not (n choose k).