       Tensor Products with Derivatives in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg121921] Tensor Products with Derivatives in Mathematica
• From: Thomas Markovich <thomasmarkovich at gmail.com>
• Date: Thu, 6 Oct 2011 04:26:05 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi,

I would like to take the tensor product of two gradient operators so
that I can construct a matrix "derivative."

This is to say that I want to do the following

\begin{pmatrix}
\partial_x \\
\partial_y \\
\partial_z
\end{pmatrix}
\begin{pmatrix}
\partial_x & \partial_y  & \partial_z
\end{pmatrix}
= \begin{pmatrix}
\partial^2_{x,x} & \partial^2_{x,y}  & \partial^2_{x,z} \\
\partial^2_{y,x}  & \partial^2_{y,y}  & \partial^2_{y,z} \\
\partial^2_{z,x}  &\partial^2_{z,y}   & \partial^2_{z,z}
\end{pmatrix}

and I have tried to do

Qt = ( {
{(=E2=80=98=E2=84=A2
=CB=9CSubscriptBox[=E2=84=A2=E2=88=82, =E2=84=A2x]# + W11), (=E2=80=98=E2=84=A2
=CB=9CSubscriptBox[=E2=84=A2=E2=88=82, =E2=84=A2y]# + W12)}
} ) &;
Q = ( {
{(=E2=80=98=E2=84=A2
=CB=9CSubscriptBox[=E2=84=A2=E2=88=82, =E2=84=A2x]# + W11)},
{(=E2=80=98=E2=84=A2
=CB=9CSubscriptBox[=E2=84=A2=E2=88=82, =E2=84=A2y]# + W12)}
} ) &;
Qt@Q

But this appears not to work. Any ideas?

Thomas



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