“Direct Product (Tensor)”的概念、定义、习题解题方法及翻译-数学辞典

单词

Direct Product (Tensor)

释义

Direct Product (Tensor)

For a first-Rank Tensor (i.e., a Vector),

(1)

which is a second-Rank Tensor. The Contraction of adirect product of first-Rank Tensors is the Scalar

(2)

For a second-Rank Tensor,

(3)

(4)

For a general Tensor, the direct product of two Tensors is a Tensor of Rank equal to the sum ofthe two initial Ranks. The direct product is Associative, but not Commutative.

References

Arfken, G. ``Contraction, Direct Product.'' §3.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 124-126, 1985.

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