$A$ and $B$ are Hermitian matrices and I am looking for a condition such that $C$ is non-singular. Can I say by Weyl's inequality that $\lambda(C)_{min}>=\lambda(A)_{min}$-$\lambda(B)_{max}$ and I somehow have that $\lambda(A)_{min}-\lambda(B)_{max}>0$ then the matrix $C$ is invertible.
P.S. If true, is there any other way to get an invertible $C$? Perhaps a weaker condition on eigenvalues of $A$ and $B$ such that $C$ is invertible.