This seems to be an eigenvector problem. If I call = one of your or , then I bring the RHS of your matrix equation to the left, I get:
I can then choose U1=1 and U2= .
Sorry, if this is the wrong subforum, firstly.
So I have a dynamical system with fixed points , and .
The bit I'm stuck on is this; I have the Jacobian matrix for and as (so the trace and the determinant ) and the eigenvalues as and .
To find the eigenvectors and I know I need to solve
and
and this is what I'm stuck on. I've found both lines of the simultaneous equations to be
but I can't get anywhere with it. I did give it a go and got but I get the feeling that's not right this was never my strong point when we initially learned it, but I think it's the complex number that's confusing me. Any ideas? Cheers in advance.