Quaternions: Extracting the Dot and Cross Products

[@hugojulianorellanarojas6762]

it's really impressive. Thank u so much.

[@TheDiverJim]

Hey Mathoma! I'm loving your video's on quaternions. They are hard for a guy like me to understand and you've done a great job explaining it. Would you PLEASE do a video on finding the angle between quaternions and the SLERP algorithm? I mentor a high school robotics team and someone who could explain this as well as you do, would be huge. Thanks for the great content.

[@arghachakraborty7088]

I do not understand why v1xv2 = -v2xv1 in the context of the video. Also why did we define the cross prod as the cross prod 7:00

[@roberth1687]

Nice to see that link between quaternions and scalar/cross product. But it's not the only derivation of the scalar product. You could derive it through vector calculation as well (see: orthogonal projection).

[@sdmartens22]

From your geometric algebra videos, the quaternion multiplication restricted to scalars zero corresponds to the geometric product with the dot product negated and the cross product in place of the wedge product. Thanks for the great content, i was wondering what programs and audio hardware do you use to make your videos?

[@Math_oma]

+Shannon Martens Indeed, this is a good observation. The quaternions, as I'll get to in my geometric algebra series, are merely a subalgebra of G(3), namely the even subalgebra (scalars and bivectors only). Quaternions, complex numbers, split-complex numbers are all groping toward the same mathematical concept. I use an external microphone for my recent videos (compare to my old set theory videos), Open Broadcast Software to capture the screen and record audio, and SmoothDraw 4 with a Wacom tablet to write.

[@Math_oma]

And I use VideoPad to edit the video, but the editing is very rudimentary.

[@ominollo]

Great explanation 👌

[@TheNewPhysics]

What is the quaternion representation of a rotation in 4D (e.g. spacetime rotation)?

[@EngineerNick]

Thankyou I found this very helpful :)

[@harishgurusamy1044]

Nice vid!! However, I wondered how u extract the dot and cross products of octonions and split-octonions. I think it would be the same procedure with the quaternions but.....

[@MaxKawula]

well explained, very help

[@styfen90]

Thank you for this great video

[@rupabasu4261]

Can anyone explain how the i,j,k componemts were taken in common to simplify the vector part

[@BlendingEdge]

Is there such thing as “Cross Product” of two quaternions ? Or is there only “Multiplication" of two quaternions which is defined as described in this video?

[@Math_oma]

+Blending Edge Cross product only makes sense in R^3 and quaternions are not R^3.

[@BlendingEdge]

@@Math_oma From what I gather the “Cross Product” makes sense only in 3 and 7 dimensions actually. (I didn’t expect that quaternions have a CP, btw, but only wanted to confirm that’s the case as I just started learning about quaternions).

[@janApen]

I'm in grade 12 and i'm loveing this.

[@jorgejimenez4325]

This is cool, but i don't see how it shows anything. How is this i-j-k business connected to the linear algebra we have now? How was this derivation of the cross product with these weird imaginary definitions translated into linear algebra, and how does this all connect back to perpendicular vectors and the area of parallelograms?

[@1conscience0dimension]

and all this already existed by nature