Given real-valued functions \{\ell_i(\cdot),\,i=1,\dots,n\} on the interval [t_0,t_f], the Gram matrix G=[G_{ij}], is given by the standard inner product on functions: .
If the vectors are centered random variables, the Gramian is approximately proportional to the covariance matrix, with the scaling determined by the number of elements in the vector.