In the fifteenth minute you say that a crossproduct between two vectors only exists in 3 dimensions, but in fact it also exists in the seventh dimension.
Ramon Debaveye In fact it exists in any 2^n -1 dimensions because there is a Cayley Algebra with dimension 2^n and we can mod out its center = (+1,-1).
I think that the direction of your arrow for e23 could be wrong, the arrow goes along the first axis in the bivector. So for e23, it should go along the e2 axis in the positive direction then go along the e3 axis in the negative direction.
Very nice and clear introduction. Note at 10:53: A father intended to name his new son John, but was advised not to do so by a friend. "Every Tom, Dick and Harry is called John"
Around 12:00 you write down the bivectors and then you make a symbolic figure: 1) Shouldn't it be a(31) not a(13) (cause of the even permutation) ? 2) Also, on the figure, the "curl" of a(12) shouldn't be clockwise ? 3) Doesn't Quaternions lead to possible 1=-1 and negative kinetic energy Hamiltonian ?
Great video! I wish you had a video on the Fourier transform in Clifford analysis. Trying to understand it and not having much luck :) en.wikipedia.org/wiki/Clifford_analysis#The_Fourier_transform
I have recently started looking at Geometric Algebra and this popped up on my feed ....thank goodness! :-)
Links that might be of interest:
Galgebra - Python library for symbolic geometric algebra -
galgebra.readthedocs.io/en/latest/
Clifford - Python library for numerical geometric algebra -
clifford.readthedocs.io/en/latest/
Marvelous presentation
In the fifteenth minute you say that a crossproduct between two vectors only exists in 3 dimensions, but in fact it also exists in the seventh dimension.
Ramon Debaveye In fact it exists in any 2^n -1 dimensions because there is a Cayley Algebra with dimension 2^n and we can mod out its center = (+1,-1).
i hope to someday soon understand why haha
I think that the direction of your arrow for e23 could be wrong, the arrow goes along the first axis in the bivector. So for e23, it should go along the e2 axis in the positive direction then go along the e3 axis in the negative direction.
Very nice and clear introduction.
Note at 10:53: A father intended to name his new son John, but was advised not to do so by a friend. "Every Tom, Dick and Harry is called John"
Ahhh The Young One's 🙂
Great Video!
However, I highly doubt, there is anyone out there, who looks up tutorials on Clifford algebra, while not knowing what a scalar is.
Unless you're like me and know NOTHING about geometrical/Clifford Algebra. Assuming makes an...ah, you know the rest...
Short&sweet, thks & request a short series.
Clifford Algebras and Spinors is a hundred bucks. Request a suitable replacement.
Very nice indeed!!!
Is there any intuitive way to compare and contrast geometric algebra with tensor algebra?
Diffuse and confused is a multivector?
Much appreciated!
Well, the cross product is dual to the wedge product, anyway.
Can you show us an concrete example. Inserting actual numbers into all the constants that would help greatly to see the algebra as a something real.
Around 12:00 you write down the bivectors and then you make a symbolic figure:
1) Shouldn't it be a(31) not a(13) (cause of the even permutation) ?
2) Also, on the figure, the "curl" of a(12) shouldn't be clockwise ?
3) Doesn't Quaternions lead to possible 1=-1 and negative kinetic energy Hamiltonian ?
clifford developed his representation precisely because of your third point.......
@@johnholmes912 Thank you for this answer, now I finished my PhD and I know a bit more :)
Please get a longer pencil its bugging me and making me feel strange the way you are holding the pencil.
E23 direction not correct.
Why don’t you brush up on your presentation? Are you trying to teach Clifford Alg to high school sophomores?
yuck...why introduce physical models, the ain't much use
PewDiePie is good
Great video! I wish you had a video on the Fourier transform in Clifford analysis. Trying to understand it and not having much luck :)
en.wikipedia.org/wiki/Clifford_analysis#The_Fourier_transform