We propose a semiparametric family of copulas based on a set of orthonormal
functions and a matrix. This new copula permits to reach values of Spearman's
Rho arbitrarily close to one without introducing a singular component.
Moreover, it encompasses several extensions of FGM copulas as well as copulas
based on partition of unity such as Bernstein or checkerboard copulas. Finally,
it is also shown that projection of arbitrary densities of copulas onto tensor
product bases can enter our framework
