I am suppose to prove that if R is a matrix, R^2 = I and lambda is an eigenvalue, then lamda is 1 or - 1
Do I somehow need to show that an eigenvector, say it is v that Rv and R^2 v ??? compared but I am lost!
Is it just that since R is squared then either 1 or -1 are values??? Frostking
A slightly different proof, without using the minimal polynomial (directly):
If is an eigenvalue of R then there exist non-zero v such that . Apply R to both sides of that equation- . But it is given that so we are saying that so that . Since v is not 0, we must have and, from that, or .