完全对称张量空间V^((m))中可合元素的一些性质

SOME PROPERTIES OF THE DECOMPOSABLE ELEMENTS IN THE mth SYMMETRIC TENSOR SPACE V(m)

本文建立了完全对称张量空间V(m)中可合元素的生成向量的坐标与一组以可合元素的坐标为系数的多项式的根之间的关系,得到了可合元素的若干必要的和充分的条件,并由此得到了表示可合元素生成向量组的方法。

In this paper, the relationship between the coordinates of the spanning vectors of a decomposable element in V^((m)) and the roots of a set of polynomials defined by the coordinates of this element is discussed. We obtain several necessary and sufficient conditions for an element to be decomposable, and, by which, Provide a method, for representing the spanning vectors of a decomposable element in V^((m)).