Vector space interference alignment (IA) is known to achieve high degrees of freedom (DoF) with infinite independent channel extensions, but its performance is largely unknown for a finite number of possibly dependent channel extensions. In this paper, we consider a K-user M_t × M_r MIMO interference channel (IC) with arbitrary number of channel extensions T and arbitrary channel diversity order L (i.e., each channel matrix is a generic linear combination of L fixed basis matrices). We study

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... maximum DoF achievable via vector space IA in the single beam case (i.e. each user sends one data stream). We prove that the total number of users K that can communicate interference-free using linear transceivers is upper bounded by NL+N^2/4, where N = {M_tT, M_rT }. An immediate consequence of this upper bound is that for a SISO IC the DoF in the single beam case is no more than {√( 5K/4), L + T/4}. When the channel extensions are independent, i.e. L achieves the maximum M_r M_t T , we show that this maximum DoF lies in [M_r+M_t-1, M_r+M_t] regardless of T. Unlike the well-studied constant MIMO IC case, the main difficulty is how to deal with a hybrid system of equations (zero-forcing condition) and inequalities (full rank condition). Our approach combines algebraic tools that deal with equations with an induction analysis that indirectly considers the inequalities.