Consider the second-order ordinary differential system $$ A y'' + i B y' - C y = 0, $$ where $A$ and $C$ are real-valued $d\times d$ SPD matrices satisfying $$ I \le A,C \le 2I, $$ and $B$ is real-valued and symmetric, having operator 2-norm less than 2 (and $i = \sqrt{-1}$). I would like to show that

1. there are $2d$ independent solution of the form $y(t) = y_0 e^{\lambda t}$ and
2. that there are exactly $d$ eigenvalues $\lambda$ having positive real part.