Experiment Do all rotations in 3D have a fixed axis?

[Deleted member 1780]

https://upload.wikimedia.org/wikipedia/commons/0/02/Rotating_Sphere.gif

A fixed axis is a line that does not move when a rotation is applied.

 

[blond_elf_bard]

I would say yes

 

[Dionysus]

3D objects don't exist

 

[quinn24]

3D objects don't exist

 

[Deleted member 1780]

I would say yes

The theorem states that any transformation (a rotation is an example of a transformation) that has an odd amount of dimensions (3 is odd) has at least one fixed axis.

So, ya.

Does any rotation matrix in 3-d space have only one non-zero eigenvector?

I know that in 2-dimension, a rotation matrix has no non-zero eigenvector. But in 3-d space, I can only imagine the rotation axis to be an eigenvector, and it looks like that the rotation angle can...

math.stackexchange.com

Rotations in 3D only have one axis of rotation as well.

These are intuitive to understand in 3D.

 

[zangano1]

I don't know

 

[RopeShow]

View attachment 135601

The theorem states that any transformation (a rotation is an example of a transformation) that has an odd amount of dimensions (3 is odd) has at least one fixed axis.

So, ya.

Does any rotation matrix in 3-d space have only one non-zero eigenvector?

I know that in 2-dimension, a rotation matrix has no non-zero eigenvector. But in 3-d space, I can only imagine the rotation axis to be an eigenvector, and it looks like that the rotation angle can...

math.stackexchange.com

Rotations in 3D only have one axis of rotation as well.

These are intuitive to understand in 3D.

Beat me to it but yeah, transforms on the rotation of 3D objects are done according to one axis, depending on how you want to rotate it.

 

[MarriedAndLookin4Fun]

Im too low IQ for this shit