A CRITERION FOR A GENERIC m £ n £ n TO HAVE RANK n

Determining the rank of a tensor has always been an interesting and important problem in algebraic complexity theory(8), algebraic statis- tics(3, 9), engineering(4) and algebraic geometry(6). In this paper, I will flrst give a criterion for a generic m £ n £ n to have rank n. Right after the criterion, the flrst application is given . Then the symmet- ric version of this criterion is formulated. In Section 4, I will give a detailed discussion of the (O(1;2) symmetric) ranks of (O(1;2) sym- metric) 3 £ 2 £ 2 tensors over the complex and real numbers with the aid of these criterions. This criterion also provides another way to at- tack the "Salmon Problem" over real numbers.