You can go on and define trivectors, etc., and the same issues show up.
So now let's talk about the classification of trivectors in 9-dimensional space.
[Typical way a math professor transitions to what they really want to talk about.]
(1/n)
John Carlos Baez on Nostr: A vector looks like an arrow; anyone studying math or physics in college learns about ...
A vector looks like an arrow; anyone studying math or physics in college learns about these. Bivectors are important too though less widely taught. You can create a bivector by taking the 'wedge product' u ∧ v of two vectors u and v, and you can visualize this as the parallelogram shown at left here. But in fact an ellipse or any other flat surface with the same area lying in the same plane is just as good a picture of this bivector. Further, you can add bivectors, so there are bivectors like u ∧ v + w ∧ z that you can't picture as just a single surface. Thus, you need to be good at the algebraic manipulation of bivectors to keep from making mistakes: unlike with vectors, the picture is just a rough indication of what's going on. Yet they are extremely important.
You can go on and define trivectors, etc., and the same issues show up.
So now let's talk about the classification of trivectors in 9-dimensional space.
[Typical way a math professor transitions to what they really want to talk about.]
(1/n)
You can go on and define trivectors, etc., and the same issues show up.
So now let's talk about the classification of trivectors in 9-dimensional space.
[Typical way a math professor transitions to what they really want to talk about.]
(1/n)