Find the eigenvalues of the rotation matrix R=(0−110)R = \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}R=(01−10) (rotation by 90°) over C\mathbb{C}C.
λ=i\lambda = iλ=i and λ=−i\lambda = -iλ=−i
λ=1\lambda = 1λ=1 and λ=−1\lambda = -1λ=−1
λ=0\lambda = 0λ=0 and λ=1\lambda = 1λ=1
No eigenvalues exist