My work requires constructing large square matrices of order 1000 as numpy arrays, whose elements are defined analytically as a function of their indices. Right now I initiate a zero array, and loop over the elements to construct my required array. This by itself takes a hefty time to evaluate. Is there any way to make the construction more efficient or faster, say by using GPU or parallel computing or the like?

What is the fastest way of doing right matrix division, i.e. xA = B in pyhton numpy? A and B are (NxN) square matrices and A is invertible, I thus want to compute equation x = BA^{-1}.