完全对称张量空间中可合元素的一个充分必要条件

In this paper,using the parameter method the author reduces the problem of the necessary and sufficient condition of decomposable elements in V^(m)to the problem of decomposability of completely symmetrical tensors of type I and type Ⅱ,by means of the equivalence transformation of decomposability of completely symmetrical tensors.It shows that the generated matrix of decomposable elements is obtained by the row elementary transformation,a necessary and sufficient condition that the type I and Ⅱ of completely symmetrical tensors are decomposable elements is also obtained.