- #1
ObsessiveMathsFreak
- 406
- 8
I'm encountering the gradient of a vector field in a problem at the moment. Not the divergence, specifically the vector.
My problem at the moment is the represenation of this using the "nabla" notation. Some authors seem to be defining this as [tex]\nabla \otimes \vec{v}[/tex], the tensor or dyadic product. But this doesn't seem to give the correct answer.
Could someone please confirm for me that the dyadic product [tex]\vec{a} \otimes \vec{b} = \vec{a} \vec{b}^T[/tex] if a and b are column vectors? What way is the gradient of a vector normally represented?
My problem at the moment is the represenation of this using the "nabla" notation. Some authors seem to be defining this as [tex]\nabla \otimes \vec{v}[/tex], the tensor or dyadic product. But this doesn't seem to give the correct answer.
Could someone please confirm for me that the dyadic product [tex]\vec{a} \otimes \vec{b} = \vec{a} \vec{b}^T[/tex] if a and b are column vectors? What way is the gradient of a vector normally represented?