Eigenvalue of a rotation matrix

[supermesh]

cos a -sin a

sin a cos a

How do I find the eigenvalue of this rotation matrix? I did the usual way, but didn't work! Could someone tell me how to start this problem?

 

[Dick]

How far did you get doing it the 'usual way'? It should work.

 

[foxjwill]

Did you try solving the characteristic polynomial?

 

[mathboy]

A rotation matrix in C^n is unitary. Unitary linear operators have eigenvalues with absolute value 1 (because unitary transformations are also normal). You will get two complex eigenvalues, both with absolute value 1. Use the high school complex quadratic formula.