“Symmetric Tensor”的概念、定义、习题解题方法及翻译-数学辞典

单词

Symmetric Tensor

释义

Symmetric Tensor

A second-Rank symmetric Tensor is defined as a Tensor for which

(1)

Any Tensor can be written as a sum of symmetric and Antisymmetric parts


			(2)

The symmetric part of a Tensor is denoted by parentheses as follows:

(3)

(4)

The product of a symmetric and an Antisymmetric Tensor is 0. This can be seen as follows. Let be Antisymmetric, so

(5)

(6)

Let

be symmetric, so

(7)

Then


			(8)

A symmetric second-Rank Tensor has Scalar invariants

			(9)
			(10)

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