Thread: 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!

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.

... a basis is . Now, normalize it.