  In [7] the authors have introduced a new construction using the Hadamard
product to present star configurations of codimension $ c $ of $\mathbb{P}^n$
and which they called Hadamard star configurations. In this paper, we introduce
a more general type of Hadamard star configuration. Any star configuration
constructed by our approach is called a weak Hadamard star configuration. We
classify weak Hadamard star configurations, and in the case $ c=n $, we
investigate the existence of a (weak) Hadamard star configuration apolar to the
generic homogeneous polynomials of degree $ d$.

Algebraic Geometry