In this paper we describe the almost complex structure as a real matrix acting on the tangent space with basis (partial derivative/partial derivative L(A(1)), ... , partial derivative/partial derivative L, (A(n))). In the cotangent space the natural Hermitian scalar product of the associated quadratic differentials (Theta(A1), ... , Theta(An)) determines a skew-symmetric real matrix C and a symmetric matrix S. We prove that the matrix of the complex structure is SC-1.