1. The problem statement, all variables and given/known data I can find my eigenvalues just fine, and they're both real, as expected. My first eigenvalue is -3, which I know is correct. I have the equations 5x+(3-i)y=0, (3+i)x+2y=0 Both of the equations come from my hermitian matrix, after I substituted λ=-3. 2. Relevant equations 3. The attempt at a solution I have absolutely no idea how to solve this. This case is simple enough to be solved by trial and error, but how would I proceed if I had harder equations? I can't use both equations since I get x=x or y=y if I substitute one into the other, since they're both the same equation.