# How to evaluate gradient of a vector? or del operator times a vector

1. Sep 15, 2010

### herbgriffin

How will i find the gradient of a vector?
i know that gradient is only for scalar to produce a vector? i am confuse since del operator is a vector how will i find the gradient of a vector.
How can i multiply a del operator and vector

2. Sep 16, 2010

### CompuChip

Usually, an expression like $$\nabla \vec v$$ doesn't make sense.
You might mean $$\nabla \cdot \vec v$$ instead, which (as a dot product) produces a scalar, or $$\nabla \times \vec v$$ which (as a cross product) produces a vector.
Only in specific contexts, the expression $$\nabla \vec v$$ may have a meaning, for example in Clifford algebras or in multi-variable analysis as a shorthand for a matrix like
$$A_{ij} = \frac{\partial \vec v_i}{\partial x_j}$$
(although I must admit I've never seen it used like that).