Proper and stable, minimal MacMillan degrees bases of rational vector spaces

The structure of proper and stable bases of rational vector spaces is investigated. We prove that ift(s)is a rational vector space, then among the proper bases of 3(s) there is a subfamily of proper bases which are 1) stable, 2) have no zeros inCbigcup {infty}and therefore are column (row) reduced at infinity, and 3) their MacMillan degree is minimum among the MacMillan degrees of all other proper bases of 3(s) and it is given by the sum of the MacMillan degrees of their columns taken separately. It is shown that this notion is the counterpart of Forney's concept of a minimal polynomial basis for the family of proper and stable bases of 3(s).