Suppose $A$ and $B$ are $n\times n$ real square matrices and further assume that $A$ and $B$ are symmetric. And now let $\lambda_A$ be the smallest eigenvalue of $A$.
Question : I want to know how $\lambda_A$ changes as we add $itB$. In other words, I want to know if there is any known fact about an eigenvalue $\lambda_{p}(t)$ of $A+itB$ such that $$\lim_{t\rightarrow 0}\lambda_{p}(t)=\lambda_A$$.
Especially, I want to know, if $|\lambda_A|\leq C$ for some $C>0$, if there is a function of $t$, $C(t)$, such that $|\lambda_p(t)|\leq C(t)$.
Thank you in advance.