When I was looking at the Gaussian Copula Example @ http://en.wikipedia.org/wiki/Copula_(probability_theory)
I realized the Gaussian Copula is stated as follow \begin{equation} C^{Gauss}_\Sigma (u) = \frac{1}{\sqrt\det{\Sigma}} \exp{\Bigg ( -\frac{1}{2} \begin{pmatrix} \Phi^{-1}(u_1) \ \dots \ \Phi^{-1}(u_d)\end{pmatrix}^T. (\Sigma^{-1} - I).\begin{pmatrix} \Phi^{-1}(u_1) \ \dots \ \Phi^{-1}(u_d)\end{pmatrix} \Bigg) } \end{equation} where $\Sigma$ is the correlation matrix, $\Phi^{-1}$ is the inverse cumulative distribution function of a standard normal and $I$ is the identity matrix.
The question is, why is there an identity matrix in the exponential form?
Thank you
