Proving Non-Zero Eigenvalues for Rotations in Euclidean Three Space

[ck22286]

Help! (Euclidean three space)

Homework Statement

Given the Euclidean three space R³and if L is a rotation about the origin, can you prove a situation when L($$\vec{v}$$)=$$\lambda$$ $$\vec{v}$$ and neither lambda or vector v equal zero

Homework Equations

The Attempt at a Solution

I understand that it is a full rotation of 2 pi but I do not know exactly how to prove it.

 

[HallsofIvy]

Think about the axis of rotation.

 

[ck22286]

Think about the axis of rotation.

I need to see how to make the proof. I understand the concept. I just do not know how to write it down in math terms.