Let $V_{1},V_{2}$ be finite dimensional complex vector space and $V=V_{1}\oplus V_{2}$. Let $h_{1},h_{2}$ be Hermitian forms on $V$ satisfying
(1) $\forall v_{i}\neq0\in V_{i} ,\; h_{i}(v_{i},v_{i})>0 \;(i=1,2)$.
(2) $x=x_{1}+x_{2},y=y_{1}+y_{2}, \, (x_{i},y_{i}\in V_{i}) \implies h_{2}(x,y)=h_{2}(x_{2},y_{2}). $
I want show that there exist $\lambda>0$ such that $h_{1}+\lambda h_{2}$ is a positive definite Hermitian form on $V.$ How to prove it?