Let A be a 2x2 matrix and let
char poly(A) = z^2 - Tz + D = 0.
Show that all eigenvalues of A have nonzero real part if T*D /= 0
Show that all eigenvalues of A have real part < 0 if D > 0 and T < 0
Based on the characteristic polynomial of A, I know that
T= a1 + a2, where a1 and a2 are eigenvalues of A
However, I do not know how to proceed from here. Any help would be greatly appreciated!!