 Positive real (1, 1)-form

A real $(1,1)$-form $\phi$ is positive whenfor every nonzero tangent vector $\xi$ of type $(1,0)$. Equivalently, the local Hermitian matrix in the representation $\phi =i{h}_{j\bar{k}}d{z}^j\wedge d{\bar{z}}^k$ is positive definite.