张量分解为矢量积之和及其意义

The Sum of the Tensor Resolution Becoming the Vector's Product and Its Meaning

证明了,在n维空间中,任何一个q阶张量(q>1)可以写成nq-1个张量之和,其中每一个张量都是由q个矢量的乘积组成。一般来说,nq-1是张量所能分解出的张量项的最小数目。这种分解可以给出高阶张量协变导数的另一种定义。

Proves that in n - dimensional space, any q order tensor（ q 〉 1 ） may be written as the sum of n^q-1 tensors, among which every tensor is composed of q vector product. Generally speaking, n^q-1 is the smallest number of the item that can he decomposed from the tensor. This decomposition may give another definition of high order tensor＇ s covariant derivative.