[Math] Minimum eigenvalue of the difference of two Hermitian matrices

Question

Consider Hermitian matrices $A$ and $B$.

Weyl's inequality tells us that $$\lambda_{\min}(A + B) \ge \lambda_{\min}(A) + \lambda_{\min}(B) $$
See this link for proof: Smallest eigenvalues of Sum of Two Positive Matrices

How can we bound $\lambda_{\min}(A – B)$, given the the eigenvalues of $A$ and $B$?

Answer 1

$\lambda_{min}(A) - \lambda_{max}(B)$?!