Let A be a 2x2 matrix with complex eigenvalue x = a-bi and an associated eigenvector v.
Show that A(Rev) = aReV + bImv and A(Imv) = -bRev + amImv
I'm really stuck.
The eigenvector associated with is .
Then and .
It's easy to see that what's been asked to be shown works here.
Since my linear algebra is terrible (and I'm short on time) I'll leave it to more expert members to prove what's been asked to be shown.