1. Complex eigenvectors

Hi!

A complex 2x2 matrix is given as

A =
a b
c d

where a, b, c and d are complex numbers.

Find the eigenvectors of U when a = 0, b = i, c = -i and d = 0, and normalize
them to unity.

I think I've found the eigenvalues to be 1 and -1. (If that is right.)
But I have problem finding the eigenvectors. I know how you should do it, and know the equation and so on, but I don't get any results. I need someone to show me how you get the answer.

Looking forward for help!

Best regards!

2. Re: Complex eigenvectors

Originally Posted by expresstrain
I think I've found the eigenvalues to be 1 and -1. (If that is right.)
Right.

But I have problem finding the eigenvectors. I know how you should do it, and know the equation and so on, but I don't get any results. I need someone to show me how you get the answer.
$\displaystyle \ker (A-I) \equiv\begin{Bmatrix} -x_1+ix_2=0\\-ix_1-x_2=0\end{matrix}$ ... a basis is $\displaystyle B_1=\{(i,1)\}$ . Now, normalize it.

$\displaystyle \ker (A+I) \equiv\ldots$