Since is almost a vector, we can think of all the ways that we can act on vectors and see how del should respond.
Vectors | Del | |
1 | Multiply by a scalar, a: | Operate on scalar f: (the gradient) |
2 | Dot product with : | Dot product with : |
3 | Cross product with : | Cross product on : |
The gradient is described in the chapter on derivatives. Below, we discuss the other operations of del.