Hi guys, this question bothers me...
I have a matrix A=
So it is a 2x2 matrix. I am asked to show that e to the power of (i theta)
and e to the power of (-i theta) are eigenvalues. Then to find eigenvectors and simple formula for A to pwr of n.
Now, I guess I should proceed finding determinant of A(with - lambda from left top to bottom right)=0. However, i can't find my way out of this. I get smth like lambda squared + sin squared theta+ cos squared theta - 2lambda cos theta=0.
Any help is appreciated!
So, how would the eigenvectors and "simple" formula turn out? Hope not anything ugly... I don't want to get stuck in anything ugly. Thx for help, though! I wish this was just a normal example I am able to do outright... but it is not.