Calculating General Tensor Product of Gradients

*To*: mathgroup at smc.vnet.net*Subject*: [mg120139] Calculating General Tensor Product of Gradients*From*: Thomas <thomasmarkovich at gmail.com>*Date*: Sat, 9 Jul 2011 07:33:53 -0400 (EDT)

Hi All, I would like to calculate the tensor product of two gradients for any coordinate system I can define, whether it be 3 dimensions or 30 but I would like to leave it as an operator so that I can apply this to a vector function and get the appropriate answer. This is to say that I want to calculate \Nabla \otimes \Nabla which in 3-D cartesian coordinates gives d_xx d_xy d_xz d_yx d_yy d_yz d_zx d_zy d_zz which can then act on a function in 3D. Well, I want to define any gradient I want (maybe prolated spheroidal coordinates, etc) and find what \Nabla \otimes \Nabla is equal to so that I can then perform further computations. Unfortunately, I have no clue how to do this and so if you guys had any suggestion as to how to do this, I would be very thankful. Best Regards, Thomas