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单词 Dyadic product
释义

Dyadic product

中文百科

并矢积

在数学特别是双线性代数中,有同样维度的两个矢量 \mathbf{u}\mathbf{v}并矢积

\mathbb{P} = \mathbf{u}\otimes\mathbf{v}

是这些矢量的张量积,而结果是阶为 2 的张量。

关于选定的基 \{\mathbf{e}_i\},并矢积 \mathbb{P} = \mathbf{u} \otimes \mathbf{v} 的分量 P_{ij} 可以定义为

P_{ij} = u_i v_j ,

这里的

\mathbf{u} = \sum_i u_i \mathbf{e}_i ,
\mathbf{v} = \sum_j v_j \mathbf{e}_j ,

\mathbb{P} = \sum_{i,j} P_{ij} \mathbf{e}_i \otimes \mathbf{e}_j .
英语百科

Dyadics 并矢积

In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra.

There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a dyadic in this context. A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it.

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更新时间:2025/6/21 22:42:31