- #1
debjit625
- 40
- 0
Homework Statement
Find the eigen values and normalized eigen vectors for the matrix
cosθ sinθ
-sinθ cosθ
2. The attempt at a solution
Well I did the eigen values hope they are correct but can't solve for eigen vectors
Eigen values are
λ = cosθ ± isinθ
on solving for eigen vector for eigen value λ = cosθ + isinθ ,I got
x + iy = 0 ,hence only solution x = y = 0 which is not the solution I guess (eigen vector can't be null vector)
or could I take y = i and x = 1 then it is solvable but again can I take imaginary numbers ?
Thanks