what are the necessary conditions for a weighted directed hypergraph to have an incidence matrix of full rank?

In this context, we can define the incidence matrix as follows:

Let $V = \{v_1,v_2,...,v_m\}$ be the set of vertices and $E = \{e_1,e_2,...,e_n\}$ be the set of edges of the weighted directed hypergraph. The $m \times n$ incidence matrix is $A = (a_{ij})$ where

$$ a_{ij} = \begin{cases} w_{ij}, & \text{if}\ v_{i} \in e_j \\ 0, & \text{otherwise} \end{cases} $$

where $w_{ij} \ne 0$ is the weight that can be negative because of the direction of the edge.

This question is a generalization of this one: Which graphs have incidence matrices of full rank?