倒三角算符

倒三角算符[1]，又称向量微分算子、Nabla算子[2]（Nabla）、Del算子[3]（del operator），符号为∇，是一个向量微分算子，但本身並非一個向量[4]。

其形式化定义为：

在维空间中，分母为含个分量的向量，因而本身就是个维向量算子。

三维情况下， 或

二维情况下， 或

作用于不同类型的量，得到的就是不同类型的新量：

直接作用于函数（不论是标量还是向量），意味着求的梯度，表示为：（标量函数的梯度为向量，向量的梯度为二阶张量）；
与非标量函数由点积符号 连接，意味着求的散度，表示为：；
与非标量（三维）函数由叉积符号连接，意味着求的旋度，表示为：。

名稱

Nabla算子的名字来自希腊语中一种被称为纳布拉琴的竖琴。相关的词汇也存在于亚拉姆语和希伯来语中。

该符号的另一常见的名称是atled，因为它是希腊字母Δ倒过来的形状。除了atled外，它还有一个名称是del。

Del算子在标准HTML中写为&nabla，而在LaTeX中为\nabla。在Unicode中，它是十进制数8711，也即十六进制数0x2207。

Del算子在数学中用于指代梯度算符，並可組成散度、旋度和拉普拉斯算子。它也用于指代微分几何中的联络（可以视为更广意义上的梯度算子）。它由哈密尔顿引入。

参见

參考

  1. ^ 物理学名词审定委员会．物理学名词 [S/OL]．全国科学技术名词审定委员会,公布. 3版．北京：科学出版社, 2019: 10. 科学文库 （页面存档备份，存于互联网档案馆）.
  2. ^ 同济大学数学系．高等数学：下册 [M]. 7版．北京：高等教育出版社, 2014: 108.
  3. ^ 史天治.狭义del算子与符号运算法[J].河南教育学院学报（自然科学版）,2007(4):16-19.维普网.
  4. ^ David J. Griffiths,Introduction to electrodynamics,Fourth edition,Pearson Education, Inc.,p.16.

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