Find the eigenvalues of cos(x) -sin(x)

[stukbv]

How do i find the eigenvalues of

cos(x) -sin(x)
sin(x) cos(x)

and

cos(x) sin(x)
sin(x) -cos(x)

Thanks

 

[micromass]

Hi stukbv!

I would start by calculating the characteristic polynomial...

 

[stukbv]

Hi, i have done that but i get L^2 - 2Lcos(x) + 1 = 0. How do i find a root??

 

[micromass]

This is a quadratic equation with unknown L. You can apply the quadratic formula on that ( http://en.wikipedia.org/wiki/Quadratic_formula#Quadratic_formula )