Any vector can be expressed as a sum of a number of other vectors. The vectors which are summed are called the components of the original vector. When you want to add and subtract two dimensional ...

Subtracting a vector is the same as adding a negative version of the vector (remember that making a vector negative means reversing its direction). \(\left( \begin ...

Any vector can be resolved into two components at right angles to each other. These two components when added together have the same effect as the initial single vector.

This note studies Hardy-type inequalities for vector fields with the L¹ norm of the operator curl. In contrast to the well-known results in the whole space for the divergence-free vector fields, we ...