  The homotopy type of the complement manifold of a complexified toric
arrangement has been investigated by d'Antonio and Delucchi in a paper that
shows the minimality of such topological space. In this work we associate to a
given toric arrangement a matrix that represents the arrangement over the
integers. Then, we consider the family of toric arrangements for which this
matrix has maximal rank. Our goal is to prove, by means of basic linear algebra
arguments, that the complement manifold of the toric arrangements that belong
to this family is diffeomorphic to that of centered toric arrangements and thus
it is a minimal topological space, too.
