Rotation in n dimension

Feb 2019
44
3
United Kingdom
Your first example is a rigid rotation in the plane/space or in more formal language a transformation of coordinates. I'm not in a position to answer the n dimensional case because I don't know, but since I've chosen the tensor route (systems independent of coordinates) I know it's going to pay off.
 
Aug 2012
2,464
761
In n dimension, you have n rotation matrices, all of them nxn?If so, how do you construct them?
If you work it out for n = 2, 3, 4 ... you'll see a pattern.

Do they look like this in 4D?
https://ksgamedev.files.wordpress.com/2010/01/matrix-rotation2.png[/QUOTE]

Could be. I only worked out n=3 once. The trick is that the n-th column of the matrix is image of the n-th standard basis vector (all zeros except 1 in the n-th coordinate).

since I've chosen the tensor route (systems independent of coordinates) I know it's going to pay off.
Can you say more about this? I know tensor products in abstract algebra, but I don't know much about the practical aspects of tensors.
 
Feb 2019
44
3
United Kingdom
What I find most illuminating about this is how does one even depict a geometrical figure in the n-dimensional case to be rotated?